What if cooler heads didn't prevail during the Trent Affair Crisis and open war ensued? Lincoln famously said "one war at a time". Could the U.S. have called on Russia who promised to help in the event of war, even leaving ships in a NY port? Would the war be the U.S., Russia, possibly Prussia to go against France?, vs C.S., British Empire, and Second French Empire?
Could the U.S. conquer Canada? Could it avoid a humiliating and catastrophic defeat? What about the war in Europe? Would a second Crimean War break out? What would be the future ramifications of British intervention in the American Civil War? I think it makes the Great Rapprochement highly unlikely.
As others have said, I don't think this will end well for the US. (Which is, of course, why cooler heads
did prevail: Lincoln was no idiot, he knew the US couldn't successfully fight both Britain and the Confederacy at the same time.)
In terms of allies, I don't expect the US to find much support in a hypothetical Trent War. For one thing, the Union's actions in seizing the ship and the diplomats onboard were widely viewed as violating international law, so the US wouldn't get much moral sympathy if they decided to fight over it. For another, America's ability to project force overseas was very limited, so it's not likely that any European country would support them on a
quid pro quo basis, because the US couldn't offer meaningful support for a European or colonial conflict And finally, this was the apogee of British naval dominance, so even if a country did want to gang up with the US to take Perfidious Albion down a peg or two, there's not much they could have done to actually harm the UK.
Britain would probably avoid getting involved in the American Civil War itself, because the Confederate cause wasn't very popular in London, and instead they'd fight a concurrent but separate war. Even then, however, such a conflict would be greatly to the Confederacy's advantage: the Union would have to divert troops to its northern frontier and east coast, and its ability to import weapons and gunpowder would be severely curtailed. Meanwhile -- assuming that Britain's first action after declaring war would be sweeping the seas free of Union vessels, which is probably a pretty safe assumption -- the Confederacy would be able to trade with the rest of the world, and also to divert the troops it had guarding its own coast (who were around 70,000 in number, IIRC) to reinforce their other fronts.
So, the Union would find itself having to defend from more directions, with less ability to equip new troops, and one of its enemies being able to reinforce their armies quite substantially. Moreover, the Union troops would be of a lower quality than their British opponents. The US' pre-war army was pretty tiny, too small to provide an adequate cadre for a force of the size raised during the USCW, meaning that the Union army was essentially raised from scratch, and inevitably, corners were cut with training. Some of this would be rectified as the soldiers served on campaign and gained more experience, but some skills couldn't really be picked up on a trial-and-error basis. Marksmanship, for example: if you're in a regiment of line infantry and you're all blasting away at the enemy, you've no way of telling whether a given enemy soldier was hit by you or someone else, or how much you might have missed by, and so you don't really have enough feedback to adjust and improve. And indeed, marksmanship in the USCW, on both sides, seems to have been much worse than in Europe: Union and Confederate troops didn't generally bother trying to shoot at ranges of greater than 200 or so yards, whereas their European equivalents might open fire at a range of 600 yards or even higher.
In short, then, it's difficult to see how a Trent War can end otherwise than really, really badly for the Union. I'd expect the Union to realise this pretty quickly, if they didn't realise it before the war actually started, and sue for peace to try and limit the damage. Britain didn't really want the war, so their terms would probably be pretty generous -- some reasonable reparations payments, the release of the ship with her crew and passengers, an official apology, and possibly some favourable trade deals as well. The real effect would be on Union morale. Even if the war ends quickly enough to cause little concrete damage to the Union war effort, going to war only to be forced into a humiliatingly quick peace is unlikely to make people feel good about their prospects against the Confederacy, and it's also likely to dent Lincoln's reputation quite a bit. Maybe it would even be enough for a peace candidate to be elected in 1864?
