Hmmm good point though I think a compromise will occur between the three, just as the CSA will become a sorta Latin analogue I envision it like Paraguay was between Brazil and Argentina in that while they won't ever close the door they won't open it given the risks.As I see it there are three scenarios.
1) Keep defending the Confederates. Advantages, keeps the US focused *mostly* on the CSA. Disadvantages, explaining to the Soldiers why they are dying so far from home when Sonora/Chihuahua are occupied by Americans.
2) Withdraw to Mexico and keep fighting. Advantages, likely to be able to retake Sonora/Chihuahuha, but will face the US exclusively when the Confederates do fall (though the entire question of whether the US will need more troops *fighting* the Confederacy or *occupying* the Confederacy is interesting.
3) Peace out. Advantages. No more Mexicans dying. Disadvantages, gives the US the time to finish off the Confederacy, the question is whether the Confederacy is too much for the US to control and whether the US will *always* have the CSA as an enemy they have to keep large numbers of troops to keep an eye on.
I'm actually expecting #3 pretty soon, especially with the Mexican *internal* pressures.
So while I do agree 2 and three are likely going to happen I do think they will they won't leave it to chance the USA won't swallow it.
Though on the topic of if the USA can occupy the CSA you do raise a concerning point, I can very much see their being a strong pull in the US to stop demobilizing given how bloody and expensive this war was than actually raise the amount of men needed to police the CSA.