As a mom of twins, I threw one birthday party for them until they were 7 or so (I forget exactly, but somewhere around then we started separate birthdays). While it was still one party, I would send an invite to my DD's invitees and a different invite to DS's invitees. They were in different preschool and elementary classes and had different friends. I never expected parents of their friends to bring two gifts...that would have been ridiculous, IMO! More gifts than I ever would want to deal with, plus why would a kid who didn't even know one of my children buy a gift for that child?
I would call the mother and ask what they would like, but work into the conversation that you don't know "x", but your son is in a class with "y." I'll bet anything she will say "it's not necessary to bring something for x." If you feel inclined to get something anyway, make it small.
I really dislike it when people say "I get both of them something smaller." Ugg. If my kids were both invited to a party, I didn't "combine" gifts...each child brought a gift of the same type/cost as if they had been the only one invited. It should work the same in reverse.