I guess I would consider why the adult is on a gluten free diet. If it's out of necessity (my youngest child has Celiac disease and believe me, I understand necessity) then you might provide something special for her, but if it's one of the new crazy "fad diet" things that are driving me nuts, then I wouldn't accommodate.
There are lots of finger foods that can be dairy free. If you are doing pizza, maybe the dairy allergic child could do breadsticks or pasta?
I wouldn't recommend baking a gluten free cake, for sure. I do them all the time because we have to, but it's very expensive and they certainly don't taste as good (at least I didn't think so at first...now I'm used to them.)
I wouldn't change your entire menu around, though...your son deserves to get what he wants on his birthday, and those of us with issues are used to having to bring our own food or miss out, honestly.
For example...at our last Christmas meal at my in-laws, my mother-in-law (who truly cares) made NOTHING we could eat. NOTHING. I suspected it would be that way, and didn't expect her to change her traditional menu for us, so I brought our own food.