There is a problem with American not-independence scenarios.
After reading extensively on the American War of Independence, its pretty clear to me that once the revolt started (and arguably it started in 1774, not the traditional date of 1775, which was when the British officially proclaimed the colonies to be in revolt), it was impossible for the British to militarily reconquer the colonies. That was the view of the British senior military leaders at the time, it was George III who insisted on even making attempt. Pre-conscription, and the British would not adopt conscription for another 140 years, they simply didn't have the manpower to conquer such a large extent of territory. They also had no clue about what political formula would reconcile the Patriots to continued British rule. They had no clue before 1775 and no clue afterwards, despite trying to start negotiations several times. The Patriots didn't help by being very stubborn in insisting on independence in all but name, and their position hardened from this after 1776. And the British were expecting another war with France and preparing for that, which also meant they could never focus on North America, even before the declaration of war on France.
So the two plausible American not-independence PODs happen before 1775. The first, which is well before, is no Whig policy of "benign neglect", so the Americans don't get accustomed to a situation where being part of the British empire amounts to contributing soldiers for various wars, timber for the Royal Navy, and providing a market for British goods (this to some extent was the situation AFTER independence) and no other demands were made on them. But this early and extreme POD butterflies much more than Mexico. The second POD, which could happen as late as 1773, is that the British either continue or resume the "benign neglect" policy. That would produce a situation where you had American filibusters into Mexico. But it is hard to see how they could have done that for long. North America before 1763 was consuming a lot of government expenditure, in the form of the few British brigades there and producing nothing in return (the customs duties were not being enforced), though having the royal officials there on salaries provided by the American legislatures would have helped in this regard. They also were complicating British attempts to strengthen their position in Canada and india and India at least was always much more lucrative.
Then the British have another problem with the colonists when anti-slavery agitation gathers steam in Britain, though here at least the British might find that the northern colonies will back them. The French revolution is another wild card.
But yeah, any POD where you can keep the Americans to the east of the Mississippi is a good situation for Mexico.