Several other considerations, all affecting cabin class and not the *G vs. UA Silver issue.
1. Make certain that you have purchased a lap child ticket for the infant (presuming that you intend the infant to be a lap child and not in its own seat with an FAA-certified carrier). While Mexico gets domestic UG privileges, paid infant tickets are still required. If you are upgraded, the infant ticket price will increase as well.
2. You did not specify the age of the non-infant child, but if the child is within unaccompanied minor age limits, that child may not be seated in another cabin without paying unaccompanied minor fees.
Thus, in order to make this work, either only one of you gets upgraded and the other sits in Y with the child and possibly lap infant or you will need 3 or 4 seats up front (depending on whether the infant is a lap infant). Because UA S would only permit one companion to be UG, you would have to purchase the other seat.
All of this a long way of saying that the likelihood of UA S upgrades are both slim and expensive.