What I do think Britain could of accomplished is a decision of how far the Americans could expand towards the west coast. Such as up to the foothills of the Rockies is most likely. Leaving the likes of Oregon as safely part of Canada, would be interesting if you could then do something further in history so that the Brits then gang up on Spain/Mexico with the yanks, yanks get Texas and Brits get California
I'm not so sure. In the early years, especially a couple of decades down the line of American independence, the Americans became quite determined of Manifest Destiny, and even if they didn't believe it was their right to rule Canada and Mexico (as people debate on here regularly) they believed adamantly that it was their destiny to rule coast to coast. Keep the USA bottled up in the East is very possible - it relies on Britain managing to enforce the rules which were supposed to prevent the USA going into Indian land where they had claims - but doing so
in collaboration with the USA is out of the question. In any such war, assuming you could somehow get the USA and the UK to come to an agreement on whether a war is virtuous enough to involve both countries, the USA would demand access to the Pacific Ocean as a minimum requirement.
This requires a POD during the early stages of the French Revolution.
The Revolution and the Revolutionary / *Napoleonic Wars are even more brutal than in OTL. As in OTL, conservative forces are eventually victorious, but by the ATL *Congress of Vienna, revolutionary ideas are regarded with such fear that the European Powers unite together to suppress any possiblity of revolution.
To secure this, as an example to the world, the monarchies of Europe prepare a joint expedition to overthrow the rebels currently occupying the American territories of his Brittannic Majesty.
Disagree. I agree in principle with the idea that the Congress of Vienna and the full extent of the Napoleonic Wars changed social views radically, but the UK never wanted to reconquer "those rebellious provincials". When the UK was fighting the ARW, it came under huge pressure from its own people - the general opinion of the average non-voting (and many voting) British citizen was that the colonies should be given their independence, and that voice was impossible to ignore. Politicians quickly came to realise that any attempt to re-impose British rule would be hugely unpopular even among backbencher MPs, let alone on the far side of the Atlantic. The British Empire was always a trading empire, with the best conditions for the British economy coming first, and retaking the USA would be massively counter-productive for the economy. The ARW was already enough to send France into a crippling spiral of debt, and they didn't commit nearly as many troops as the UK would need to annex the USA, and they were only involved for 5 years, too. On top of that, as soon as the USA became independent, it sent virtually all of its trade (where the money was to be made) back to Britain. Even better, even, since as foreign nationals, the American merchants could be taxed into the ground with foreign duties and tariffs against non-British traders. This money meant that the British Empire made about as much money post-independence as it did when it owned the whole area.
On top of this you should remember that the UK had no zeal for suppressing American republicism. There was very little call for an overthrow of the British monarchy, mainly because Parliament had become powerful enough even by this point that to most non-extremist libertarians, the UK was "the" example of how to run a democratic state. Sure, there were problems and the instability of the King posed problems, but when Parliament was so powerful there was no reason to ask questions about King or President. To the UK, the USA wasn't a threat, and it's influence on the French revolution was both too late to prevent and just a little too protracted to call for the dissolution of the entire USA. Even the most monarchically minded British men simply looked at the USA, laughed, claimed it would collapse under its own weight and held it up as an example of how republics founded upon overthrowing monarchic rule were doomed to failure. Note incidentally that in the present day, many are still predicting that the overenthusiastic approach of American republicism will cause the US to collapse or suffer a massive blow in the vague future, and it's a view I myself can't entirely discredit. Read into that what you will.
Basically, for the UK there was just no interest in reconquering the USA. If you want the UK to keep ruling the colonies, your latest POD must be in the early stages of the ARW itself. Your best bet is to find a way to butterfly away the entire independence movement wholesale.