Actually, now that I think about it, I believe there was a series called "Pax Americana" aired a couple years ago about a similar subject, but it lost popularity quickly due to its lack of plausibility. (Then again, the script writer was Harold Dove, so of course we ought to expect that.) The stabilization of the government with a new constitution being put together was an interesting way of solving the problems with the earlier systems, and some of the earlier parts, like the American Civil War arc, were pretty innovative, but the parallelism after that was kinda stupid and the American attempts at imperialism later on and the pointless, contrived war against Spain were what kind of broke the series for me. I stopped watching after that, but I looked up a plot summary of the other seasons later, and the same thing as you're suggesting here happened, with the Americans aligning with the Entente during a blatant reskin of the Weltkrieg. It was about as unoriginal as you'd expect- France working themselves up into a fervor over Germany taking one tiny province, Germany trying to invade France by going through a neutral nation (does Dove expect us to believe that the Germans are suicidal or just too stupid to realize that'd bring in Britain?), and Russia falls to a leftist revolution for... what reason other than "totally not contrived plot twist," exactly? The "World War II" arc (God, the unoriginal names for the wars make me cringe) was basically just Dove repeatedly shouting "HAHAHAHAHAHA LOOK GUYS THE RIGHT WING IS EVIL AND WANTS TO KILL EVERYONE" and was clearly implausible even if you don't have a decent grasp of geopolitics- I really don't know how his scripts made it past the editors. The only thing I thought was interesting there was how Italy was handled during the period between the world wars, but its performance in WWII was lackluster and disappointing. As goes without saying, the series was cancelled at the end of the WWII arc due to poor ratings.
Setting aside ranting about fiction, no American expansion north would have definitely improved Anglo-American relations, but assuming that the Weltkrieg still happens (which it could just as easily not) America would probably stay neutral due to conflicting interests on both sides. If they did join a side, they'd have to have a valid reason that they'd given considerable thought- perhaps a diplomatic incident leading to the assassination of an American ambassador as in OTL could do it, though the timing of the Americans joining the war would be the most important thing to consider.
