An attempt to bang together a timeline.
"A Very Different 1862"
Jan 62: London receives Lincoln's refusal to release the prisoners. The country is in uproar. Palmerston authorises the activation of the Militia, approves the plan to allow the Volunteer Army to send volunteers and sanctions the Particular Service Squadrons to sail. Canadian Militia are called out en mass, around 25% of the Canadian Beat Militia respond (this is roughly historical).
Feb 62: Goldsborough is no fool. He abandons the blockade and ships as many men to New England as possible, concentrating his forces at Hampton Roads in the Chesapeake. Milne hits him there, the Battle of Hampton Roads is a major British victory. Border raids occur around Canada. Fort Detroit and Fort Montgomery (neither of which are well garrisoned) fall to the British. Fort Monroe comes under naval bombardment from British armoured warships, although reduced, the Fort refuses surrender, and Milne hasn't the land forces for a ground assault. He withdraws, leaving a blockading squadron. In New York, USS Monitor is commissioned and remains in NY harbour, expecting a British attack. Grant starts his penetration of the Mississippi and Cumberland Rivers, capturing Nashville.
Mar 62: With the forces evacuated from the South, the Union forms the Army of the St. Lawrence, Ambrose Burnside commanding, with Sherman as his second. They move north, invest and overwhelm Fort Montgomery with severe casualties. The British blockade of the Union is completed. News starts to reach other outposts. The British and American West African Squadrons fight an action that is essentially a series of single ship duels, resulting in Americas first naval victory of the war, although the Americans are forced to quit and steam for America. McClellan's Peninsula campaign is nigh on impossible, Fort Monroe has fallen to Johnston's Army of Northern Virginia, instead
April 62: The St Lawrence opens to navigation, tens of thousands of British regulars pour into Montreal. The Union Army of the St. Lawrence advances in Canada, seeking to cut the Beauharnois Canal by aiming straight for Montreal. Burnside's 50,000 man Army meets 25,000 British regulars, plus a similiar number of Canadian militia and is repulsed making a series of bloody frontal assaults at British prepared positions. Burnside withdraws from Canada towards Lake Champlain, but loses a considerable number of troops during the march to British cavalry. American newspapers consider the horror of the battle shocking.
USS Galena is commissioned, and joins Monitor in defending NY. Lincoln calls for 300,000 new enlistments, they start trickling in as states form new Volunteer Regiments.
In the West, Shiloh does occur on schedule, however, with no possibility of a naval attack on New Orleans, Johnston is able to spare an additional 15,000 men for the assault, and has gunboats on the Tennessee, while the Union is a Division weaker than in OTL. Hardee's Corps flanks the Federals and Grant is reduced to an orbis against the river, Wallace's Division is beaten off. On the 2nd day, Buell's Army does not cross the Tennessee, but rather covers the withdrawal of the remainder of Grant's Army, before CS gunboats cut them off. Shiloh is a stunning victory for the CS, with 10,000 casualties to 30,000 Yankees (mostly captured when they couldn't cross the Tennessee). The remaining Federals fall back to Nashville. Johnston pursues and the Union withdraws from Nashville.
In the Eastern theatre, the other Johnston is sent as special advisor to Milne, leaving General Lee in command of the Army of Northern Virginia (well, I had too....). Lee decides to settle this war by invading the north and makes his preparations.
The CO, Vancouver, blockades San Francisco.
May 62: Lee attacks McClellan's Army of the Potomac around Manassas junction in what history would call the 2nd battle of Manassas. McClellan's Army is dispersed, trying to defend all axis of approach to Washington, and his 60,000 man wing at Manassas is facing an Army of Northern Virginia reinforced by forces previously containing the Union in the Carolinas and Georgia. Lee's 90,000 men smash Pope's Wing, but Lee is not able to convert this into the complete destruction of Pope. With Pope out of the way, Lee moves to invade the North.
Johnston, in talks with Milne, agrees to have the CS support a British amphibious assault on Baltimore, while the AoP is busy with Lee in June.
In the West, the other Johnston decides to invade Kentucky. A detachment under Bragg recaptures Forts Henry and Donaldson. Johnston advances on Bowling Green, and engages Buells Army of the Ohio (which has incorporated the remains of Grant's Army of the Tennessee), while Beauregard takes a detachment and seizes Munfordville. While tactically Buell does better than Johnston, he is massively outnumbered, and on hearing Munfordville (his line of supply and retreat) has fallen, is forced to surrender his Army, ending the campaign for Kentucky.
The Army of Nova Scotia (20,000 regulars and 30,000 militia), noting that Maine did not decided to seceed, advances to Portland, and secures the Eastern terminus of the Canadian Grand Trunk railway. Williams detachs off an "Army of Michigan" (20,000 regulars and 10,000 militia volunteers) to campaign in the area of Detroit, leaving him with just 20,000 regulars and 30,000 militia in the vinicity of Montreal, and just 20,000 militia on the Niagara peninsula.
The governor of Manitoba makes an adventure into Minnesota, with a column of just 4,000, including just one regular British regiment but many French speaking Canadians and Indians.
An Army arrives at San Francisco from India (30,000). Find the port defences too tough, the Army lands 5 miles up the coast, and takes San Francisco by land.
Monitor, Galena and a number of small Wooden ships sortee against the British at Long Island Sound. The British, aware of Monitor, have placed an Armoured Frigate covering this approach, HMS Defence, in addition to several wooden warships (including 2 Steam Liners and a Large Frigate). The Monitor finds she can't hurt Defence, while the same is true the other way around. However, after 2 hours, a 68 pounder ball from Defence strikes Monitors thinly armoured deck and pierces, an hour later Monitor flounders due to taking on too much water. Galena finds her armour totally ineffective. HMS Queen rakes her for 20 minutes before finally boarding and taking her a prize.
June 62
Burnside has rebuilt his Army. He now has 60,000 men, mostly new recruits who've been in the Army 6 weeks. He doubts his ability to take Montreal, and so digs in. Burnside and Williams face each other off.
The Army of Nova Scotia finds that the people of Maine aren't too averse to the occupation. They even manage to raise a brigade of local troops (mostly from the garrison that surrendered). The Maine born Joseph Chamberlin is appointed Colonel of the King's Maine Regiment, attached directly to the Army as they start to head further west, amazed by the lack of resistance. New Hampshire falls with hardly a shot being fired, and it isn't until they reach the Green Mountains of Vermont that raids on their supply lines by local partisans stop their advance.
Lee's invasion of the north begins. Lee immediately suffers when many of his men refuse to invade the north, reducing his Army to 75,000 men. Crossing the Blue Ridge near South Mountain, and sweeping away McClellan's detachments, he is intercepted near Sharpsburg. The Battle of Sharpsburg is a resounding Confederate Victory,since McClellan is actually slightly outnumbered (75,000 CSA vs 70,000 USA) and considerably outgeneralled, Longstreet's Corps makes a wide right flanking maneouvre, enveloping the Federal left, while Stuart's Cavalry Corps moves to cut off the retreat. McClellan withdraws up the Hagerstown Pike, consolidating to the North with only 40,000 men. He then moves East towards Gettysburg where he hopes to turn south and reunite his army.
Meanwhile, at Baltimore, Milne's squadron reduces the defences of the Harbour and he lands Marines and troops, 6,000 of them. Wool's Division moves to meet them in fierce house to house fighting, but his superior numbers (10,000) are without combat experience. The British seize Baltimore.
Lee wastes no time. Detaching a wing of his Army under Jackson (20,000) to pursue McClellan, he takes the remaining 45,000 towards Washington. Jackson engages in another battle with McClellan at Hagerstown, with McClellan trying to entrain his army. McClellan gets 20,000 out, while the remaining 20,000 are casualties or captured by Jackson. Knowing he can do no more good here. Jackson marchs east to rejoin Lee.
Lee heads for Baltimore, linking up with the British, from there they advance towards Washington.
July 62:
The Siege of Washington
Washington is extremely well fortified, and is considered to be tougher than Sevastapol was. The British however know how to conduct a seige, and they're brought along a large siege train. The Siege of Washington will continue for several months yet.
In the West, Johnston decides he won't be upstaged by Lee. He decides to make not one, but two offensives. One up the Mississippi to St. Louis and one up the Ohio to Cinncinnati (under Beauregard). Given the confused state of the Union forces in the theatre, and the new riverine gunboats the CS has purchased off the British he is wildly successful.
August 62
The Siege of Washington continues, McClellan withdraws accross the Susquehanna, trying to consolidate and gather all the men he can.
Meanwhile, the Nova Scotian Army has crossed Vermont and Burnside has decided the time is right to move on them. . He orders a concentration against them, with his Army. Burnsides 75,000 are confronted by 15,000 British regulars and 25,000 Canadians. They even include a small number of Americans who've enlisted. Burnside shows he's learnt his lessons well, but despite inflicting more casualties than he receives (8,000 British vs 5,000 Americans) he is forced to quit the field to avoid encirclement when Williams Army pursues him. 8 days later another battle occurs in the Hudson River valley, with Burnside on the defensive. He stops the British at the cost of 20,000 men (vs 20,000 Brits), and withdraws further to cover New York City and Boston.
September 62
Washington falls. Despite everything, the US still do not surrender and Lincoln, now in New York, vows to continue fighting.
Johnston reaches and captures Pittsburgh, cutting the US in two.
All that remains is the final act. Since the US won't surrender, Philadelphia, New York City and Boston must be taken.
USS New Ironsides is commissioned at Philadelphia
October 62
Milne leads 7 armoured frigates into Boston Harbour, at the head of the British fleet. He reduces Boston and raids the Harbour, taking many prizes and firing the remainder before withdrawing.
New York explodes. The war has always been deeply unpopular there and the Mayor of NYC declares New York an Open City, effectively secceeding and avoiding a British attack.
November 62
Lincoln, on board USS New Ironsides, meets Admiral Milne and General Lee off Philadelphia. He offers the surrender of the United States.
In the coming negotiations, the CS gain recognition, and include the New Mexico, Arizonia, Indian Territories, as well as Maryland, Missouri, Kentucky and the return of Western Virginia.
The US recognises the independence of California and the other western provinces (under effective suzerainity of the British), the Independence of Indian territories around the Dakotas and Minnesota (again, under effective British suzerainity), New York City, and the annexation of New England by the British.
Long term, the US never becomes a Great Power. Denied the west, and the money it brings in there was never the economic draw to bring in new settlers. In 1914, the US population was only 24 million, against 25 million in Greater California and 31 million (including the now freed Blacks in the CSA following the 1867 ruling that every Negro child born after that date was considered Free).
Britain declares war because the Us refuses to apologise for breaking international law in the Trent incident. The US is blockaged and border fighting occurs. British actions will probably be largely defencive. However if, as suggested by most Americans, the US refuses to come to terms it will probably start using its naval mobility to raid or attack isolated areas where it can easily outnumber the Americans. I don't expect Britain will start using the sort of burnt earth policies the US used in defeating the Confederacy. [Possibly if the Us makes large scale destructive raids into Canada but even in 1814 we showed a lot of restrained at Washington]. If the US continues for more than a couple of years things may get rough but the primary damage will be to the US economy from the bloackage and its own actions. In those circumstances I could see Britain regaining what's now Washington state and possibly some minor border changes. Think it would take a long and bloody war, with a very obstinate US to get the sort of border changes 67th Tigers mentioned in his extreme scenario. If so there might be long hostility toward Britain, amongst others, but the US would be a lot weaker than anything in our timeline.