"My son's cat."
Translation:Cat mo mhic.
It has more to do with what/who is possessing what/whom and not the number.
It helps me to think of the genitive case as "X of Y" instead of "Y's X." In this sentence, it is the son who owns the cat, so it's "the cat of my son", where the order of "cat" and "son" is the opposite of "my son's cat."