It's a bit of hyperbole to say that the Union completely collapsed. They did lose New York and New England in the aftermath, but that is nothing compared to what was wrought on the Confederacy. The squabbling states of the South soon splintered into the majority of those disparate nations - Texas, Sequoyah, Louisiana, Virginia, and the Upper South Alliance all split off in their separate ways to proclaim independence from the rump Confederate government. It was only the secession of dissolution of New England and the temporary independence of Michigan that brought the total number to twelve - the main belt from Pennsylvania to California remained as one unit. One very troublesome and fractured unit, but one all the same.
Though, the resurgence of the native tribes, however temporarily, brought that number much higher at times, though many of those independent republics are shortlived. We're also discounting the various "county-states" that emerged in the south, the quasi-governments of East Tennessee (whose lack of federal assistance in putting down led to NC and TN to leave the Confederacy and form their own alliance). In total, the number of states in total probably encroached upon the hundreds, though, in general, we're limited to the twelve as mentioned.
And the remainder of the events after the Third Revolution (the misnomer applied to the British-New Yorker War) were to have happened regardless. French encroachment and influence was detested by the Union's government, and probably would have been a trigger for war.
That, or Spanish inroads into the Confederate rump could have also caused some event as well. The Confederate-Spanish broke out in 1893 when a Confederate warship was boarded by Spanish collectors, and in the process the Spanish opened fire on the ship as it tried to escape, and on Charleston as well. As poor as the Confederates were, they had no hope but to invite in the victorious Union, who had just managed to make arrangements with the readmittance of Virginia into the union (with Virginia's debts to Britain being forgiven as part of the price of the Third Revolution).
So, in the end, I certainly see the Union reuniting the majority of their land. Now, they might not retake all of New England - Massachusetts "was" trying to increase ties to England, taking New Hampshire and Maine with it, and the Confederacy could certainly remain a backwards rump as well. They were one of the former states that whose readmittance caused contention within the Union - it was incredibly backwards and poor compared to even the other former confederate states.
So perhaps the Confederate-Spanish war becomes the American-Spanish War, but instead of aiming to reannex the south, the Union wishes merely to keep it in its sphere. This may avert the admittance of Cuba into the union as a balance against the poorer southern states.