Can you explain, what does this mean?
The US will attack Canada first since it's the most dangerous threat they face and the one easiest to take. Once Canada is done, the US will sit back, build up the Navy, and then take care of the British (and French) in the Caribbean, island hopping to Trinidad (key oil source). Bermuda will fall shortly after. The US will also ensure that the Germans do better in Africa and get their colonies back at the very least, no strings attached. Odds are good that the US Navy will eventually strike out into the Pacific and start taking British islands if given the chance, but I think that the British will be defeated by the point the US can launch a campaign there (and early on, the Anglo-Japanese alliance will keep the US and the small German Pacific squadron on the defensive, but I expect the Japanese will bow out given 2-3 US victories since they can't commit to a sustained war against a major power like the US at that point).
After the war the British Empire is screwed since the US will make sure chunks of it are handed to Germany (Zanzibar, some West African colonies, etc.), some are given independence (Boers), and the US will annex quite a bit--all British and French Caribbean islands (I don't see the Germans getting any) and at the very least British Columbia. Canada is divided into three republics (Ontario+Prairies--assuming the Prairie Provinces aren't annexed too, Quebec, and the Maritimes), Newfoundland will become independent. Guyana will probably be handed to the US as well, while Belize is annexed by Guatemala. Brazil will likely annex French Guiana assuming they were allied to the US (Latin America in the early 20th century is very US influenced, but there's still a lot of British influence, so an Anglo-American War could easily spark a lot of conflict in Latin America).
So yes, when Canada is gone, the rest of the British Empire is next. This TL's US Marines will be just as famous for their exploits in the Caribbean as OTL's US Marines are in the Pacific.
Re supplies.. I am thinking that the Canadians and UK will have had decades to think thru how this conflict might play out and it seems reasonable to me that considerable quantities of food, coal, other fuels, fodder for animals, medical supplies etc could be stock piled in likely areas where their armies may need to make a final stand. I suspect munitions will need to be shipped in. Ideally from the UK perspective as few civilians as possible would be behind their lines at this stage.
So does the US, that larger army has wargamed this scenario and has a lot more officers able to make their voice. They have years of experience in guerilla warfare against the American Indians.
I am also envisioning that towards the end of the campaign if their main positions are in danger of falling the UK might land forces by sea in places such as Churchill Manitoba (along with a reasonable quantity of supplies) and basically uses them as bait to force the US to invest resources into either reaching these locations over land or entice the USN into trying to reach them by sea where the RN can attack them along the way. Even if the fortunes of the RN are starting to fall by this point, mines, submarines, light forces and probably general navigational hazards will present issues for the US. I suspect the US would also have to invest significant resources into preventing the RN from occasionally re supplying these forces by sea and that diversion of US naval forces will also help the UK.
True, we're talking about the same US which committed to the Aleutians Campaign, but resupplying any force in Churchill or any far north Canada port is simply pointless in the scheme of things. A US geared up to war production won't find much problem sending a few ships to patrol against the UK--or early aircraft. In the far north, icebreakers will be an interesting factor since the US will have experience with them during the campaign on the Great Lakes. Any amount of equipment or personnel lost at that point is replaceable.
I agree the UK will make a huge effort to hold the maritimes region (and probably Vancouver island if the Japanese can help.)
Japan has nothing to gain helping the British in the Western Hemisphere. They have little to gain at all once the US joins the war since once the US gears for war, Japan can be sure they won't gain a thing (since the US will try and help Germany out at the peace settlement against Japan) and could lose quite a bit (starting with the IJN). An invasion of Hawaii will almost certainly be defeated. The Philippines will be challenging to hold for the US, but if the US is seriously preparing for a war against Britain, then they've made plans for the Phillippines too which will make it very, very challenging for Japan to take (although could rely too much on local soldiers).
I do not necessarily disagree with you about the broader strategic issues for the UK, but I expect the UK would want to keep the war going in and around North America as long as they could as they could.
Good luck at that, since it will send many Royal Navy sailors to their graves by 1915/1916 trying to relieve Halifax or the Caribbean. They'll take down a lot of Americans in the process, but between the lack of oil (oil-fired USN ships will dominate their coal-fired RN ships) and the distance the US Navy and the US Marines will win again and again in the Caribbean (in addition to the final defeat in Canada). It's enough to make Britain question why they're even fighting, when the German-American alliance is clearly dominating. Britain is not stupid--they will find a place in this new German-American world.
I also would not discount the UK trying to seize US territory (perhaps in areas such as the Gulf of Mexico, or maybe the pacific coast if the Japanese can help) to force the US to devote more forces to ejecting the invaders. As I mentioned before I also suspect the US holdings in the Pacific will be rather different in this time line which may help the UK and Japan.
Yes, the US holdings will be different, as in bigger at the cost of the British and French. Japan's half-hearted interest in the Great War means a solid defeat or two at American hands means they'll quit the war. Japan is not a solid ally for the Entente.
I would have to think thru the likely frontages vis a vis the likely size of the US and UK forces but I would expect the UK to have an advantage if they are fighting defensively over ground that they have spent decades planning to defend. At the end of the day if the UK can tie down significantly more US forces than the UK needs to station in Canada then I expect the UK will believe their efforts are worth while. If the US is determined to eject the UK from ALL of Canada by force then I believe this is probably a good outcome for the UK as it will tie down more US forces. If the US is smarter they will simply try to isolate and contain the residual forces in Canada once they have obtained a reasonable set of war aims.
The US cannot land many forces in Europe, unless Spain is allied to the CP. The GIUK gap ensures very few Americans will arrive in Europe, likely no more than a division at best. Instead, the might of the United States will be unleashed on the British Empire, starting with Canada. And this is very bad for the Entente. Not a single Canadian soldier will arrive in Europe. The UK will devote their resources toward supplying the war in Canada. Some pre-war Royal Navy buildup will go toward defending Canada, in a hopeless quest against the US buildup (US Great Lakes shipbuilding was dominant vs Canada's shipbuilding there and the US has no desire to let the Anglo-Canadians eclipse them there).
After Canada comes the Caribbean, including Belize, Bermuda, and Guyana. Then the Pacific colonies of Britain and France. Then Africa--Liberia will get a shot in the arm.
Basically everything between Lake Superior and the BC coastal range can be taken by the USA with minimal resistance - its lots of emptiness with few terrain features other than the Rockies and low population. The coastal area of BC and Victoria benefits from RN support, and maybe the IJN helps however the only logistic support is whatever is stockpiled at bases there, and the ability to repair battle damage is minimal, whereas any US battle damage is readily repaired in Seattle or San Francisco and logistical support is functionally unlimited. even if the UK/Japan take Hawaii, that has a limited benefit for supporting BC by threatening raids against the West Coast. The Eastern Great Lakes shores will be heavily defended (think of facing fortifications between Detroit and Windsor) and Halifax will be a fortress. The problem will be the USA can attack from the west, from the south, and force the Canadians to defend the entire lake shore as the US will rapidly have naval dominance. Isolated pockets can hold out, but food, munitions, and manpower will all become issues fairly quickly it is questionable how much money the UK/Canada can or will invest in stockpiles.
IJN can't be counted on IMO. And the Great Lakes will either result in early American victories, or early British victories (against all odds) followed by the Americans overwhelming the British through sheer industrial capacity.
IMHO if the USA is with the CP, then the Italians will stay neutral until they are pretty sure of the winning side, which puts an extra burden on the MN and RN in the Med. A CP USA won't be providing any loans to the Entente, nor will they be source for food or any manufactured goods let alone military equipment - all of that was the major US contribution 1914-17. Nobody else can make up this deficit, and even if you have an independent CSA like in the Turtledove series, they certainly can't fill in for what the USA produced/loaned, and trade from such a CSA to the Entente would be as difficult as British reinforcement of Canada. To the extent there are blockade runners or merchant submarines, some of the shortages in Germany can be alleviated.
In the 1910s, Irish, German, and Italian Americans could be a potent anti-British force domestically, and I wouldn't be surprised that by early 1916, the global war will be looking very poor for the Entente side, and then in comes the Italians, having waited for this opportunity--Nice and Corsica will be their's by the end of things no doubt.
One possibility for the USA throwing in with the CP, where the CSA does not exist, is a more CP leaning USA to begin with where the irritation at the type and scope of the British blockade is not acceptable and the USA sends an escorted convoy of humanitarian goods to Germany or even a neutral port for transshipment and the RN attempts to block the escorted convoy. Shots are fired, losses on both sides, and away we go...
I would love to see a "Channel Dash" type battle where the US sends a fleet through the English Channel to dock somewhere in occupied Belgium as a challenge to the Royal Navy, which causes a major sortie, which results in one side being dashed against the White Cliffs of Dover in utter defeat.