I live in the United States.
Let's say that Spain has a better time of it in its Napoleonic alliance with France. Things go well enough that there's no need for anyone to trade Louisiana for cash, and in the great Anglo-French struggle Iberia is pretty much uncontestedly Continental. The British are generally successful in the Caribbean, though, and eventually invade Florida. The USA, led by the Republicans, at this point decisively joins the Franco-Spanish alliance and, besides dispatching forces to relieve the defenders of Florida, also invades Canada. The British sea power is devastating to the USA's maritime areas (the national capital, in a supposedly temporary move, is shifted from Washington to a less exposed part of Pennsylvania), but the continental campaign is a great success: Quebec and all higher lands fall to America. Britain, however, retains Rupert's Land and the Maritimes. In the south, American arms are no less successful, but there the aim is purely the defense of an ally, and the stars do not align for Florida or New Orleans to be added to the Republic.
An American political consensus emerges whereby the federal government supports internal improvements which, by quirks of geography and politics, mainly connect the West and the North. So popular are these roads and canals in the West that protectionist tariffs in support of Northern industry (at the expense of consumers of such industrial goods) can be passed. And the West is getting bigger: the Viceroyalty of New Spain has downsized by selling off the underdeveloped northern part of Louisiana to the United States, though not the strategically valuable southern part. American slavery has not been able to expand, and as abolitionists gain a following in the North fire-eaters start sounding more reasonable in the South. Everything culminates in a civil war on similar lines to ours, but a few decades earlier. The absent capital gives Maryland (not to mention Delaware) the chance to secede along with the states farther south, and moreover this *Confederacy makes its secession stick.
The late 19th century sees a series of brushfire wars between New Spain and the Union over what we know as the Western United States. The USA never actually annexes New Orleans, instead propping up a satellite state guaranteed to allow trade through on the Mississippi. But the last of these conflicts is merely one front of a massive, industrial worldwide war, of which New Spain is on the winning side and the USA is on the losing. Although the Union does not fall to its enemies, it is forced to withdraw from its sphere of influence, and its disappointed populace turns to radical politics.
The Presidency is allowed copious emergency powers to deal with the violence and disruption stemming from paramilitaries with conflicting ideas on reforming society. This backfires on the establishment when a President hostile to the idea of private capital is elected, though not without myriad voting irregularities. Thus the violence is not ended, merely crystallized into a war between those holding to the legitimacy of the election (largely, the leaders of the states from the Appalachians west) and those denying it (concentrated in New York and New England). International intervention (not coincidentally, by powers with investments in New York) saves New York City from falling under the control of this regime, but does not dislodge it; instead, New York, New Jersey, and the New England states abandon the American project as a new federation.
The borders of North America eventually stabilize there, more or less, with the USA's eastern and southern splinter states not reintegrating under its sovereignty. The one big change in the later 20th century is the awakening of the national (i.e. linguistic) consciousness of Quebec, which results in its own secession. By the present day, the USA has a seaport at Philadelphia, but it is cut off from direct coastline access by the latter-day "Dominion of New England"; north of that is that independent Quebecois state, which abuts the onetime lands of the Hudson's Bay Company, now an independent state stretching from the eponymous body of water to the Rocky Mountains. Adjoining that is the once-disputed Oregon Country, home to a long and convoluted history that does not involve permanent American annexation, but coexistence with its neighbor New Spain, controlling territories that reach all the way to those of the *CSA. And that nation, of course, also extends to the Delaware River.