As you are on separate airlines each way, this is not likely to be a problem unless there is some code-sharing link between them. If Airline A is really distinct from Airline B, then it should not impact your trip home.

The luggage thing...it's best not to check it, or your luggage will go on without you. Pack light.

Otherwise, as the previous poster said, find out if you have to clear Mexican customs at MEX..in which case you get to claim your luggage before it goes onto CUN.