I doubt the US is going to be picking up any Mexican Territory in this war; its been suggested before that Mexico leaves the war with a white peace or, at least, something so close to it that it doesn't matter. My personal feelings is that Mexico, by the time it becomes evident that the war is lost, holds a bargining chip or two (be it either parts of SoCal or the canal itself) that they are able to get very good terms indeed. Coupled with the fact that Mexico's army behaves very professionally, especially in comparison to to the Confederates, there doesn't seem to be too much desire on the part of the US to overly punish the Empire for it's involvement in the war.
As for Kentucky; I'm not sure that the US would really want any territories which are majority freemen. They're going to be dealing with a refugee crisis, as former slaves are fleeing into the US to escape the Southrons - and we can only imagine the types of headaches this is going to cause - and willingly adding more Freedmen as a result seems like something that the government would be less than keen on. Remember that, though this US is less overtly racist than the ATL US during the same period, it is hardly a utopia either. Liberals (and Dems!) can, and have, spoken about the need for abolition - but there is a big gap between that, offering sanctuary to the former slaves who request it, and willingly annexing a state comprised primarily of ex-slave refugees. Though the lessened racial tensions in the *US stem from the failed Civil War and an effort by Americans to differentiate themselves from their Southron cousins, it also is because the African-American population is significantly smaller in the Union and, as a result, they are not seen as a threat (the fact that most of those who are there are loyal Liberals doesn't hurt matters either). I suspect that once we see a major immigration of Freedmen into the US, there's sadly going to be an upswing in racial animosity towards the newcomers; and adding parts of Kentucky or Tennessee in this type of scenerio would make that worse