Dear Pam,
I think the Mexicans approach in the actual attack of the states would determine if both the US and CSA would have been the attacked part(ies).
If so, an alliance between them would likely be made. There is many aspects of this too, because New Mexico and Arizona was a battleground during then "the late War". It may have ended up in one maybe had become allied with Mexico instead - my bet to that it would have been the US.
The reason to that is that I think England and France would have taken sides with CSA in this struggle.
Roy H