My eldest 2 boys are only 16 months apart and I'm finding this situation occuring a bit lately. Sometimes they both get invited but mainly its one or the other. I try to just make the one that is invited go as I feel it is a special time for him, and the parties do tend to even out so it isn't like the other child never gets to go to a party.

If I was really stuck and it was at a play centre I would ring the Mum and just see if she was ok with it. As you said you would be paying for your other child anyway.