How would you handle this situation?

Perhaps you could find a gift item which does not involve eating. That might help. Or perhaps you could find a recipe that is not fattening. I think what you're doing is wonderful and so very thoughtful and sweet. I understand where that other lady is coming from as well and I know you do too. But you're right. She should be the one to tell her daughter and it doesn't seem fair that she's left out when all the others are eating in front of her so that's why I suggested finding a non-editable gift idea.

Ask her mother if it would be OK to have a fresh fruit or cheese & meat platter type thing for her birthday. As far as being fair ,it’s not good to sabotage someone’s healthy diet either. When the boy was in second grade his teacher encouraged parents to bring cupcakes to school on their child’s birthday. She let them have them the last 30 minutes of the day before they went home. I always knew when he had eaten those cupcakes because he would be hyper and clumsily knock things over. I was glad when he went to third grade and that mess stopped. I make him cupcakes and things but not an inch of icing on top and sometimes use low carb sweeteners like stevia so I can have some too. No problems with that. And the food dyes were probably a problem with the hyper thing too.

I bake cakes with honey and yoghurt as a healthy alternative for kids. Popcorn also goes down well. Tbh, I'm not a great fan of putting lots of sugar into children, even the very active ones, as the consequences are frequentky very ugly. But your baking is very kind and I think that parent was a bit rude to expect you to deal with her daughter.

she can have a rice cake while everyone else has cupcakes.

I'm afraid having to leave people out for one reason or another is a fact of life. I don't expect people to accommodate me and provide non-alcoholic, low sodium, non-cola, non-aspartame, non-Nestlé options for me, and I'd rather just go without than have people bend over backwards, worrying about being good hosts

I think thats the parents responsibility to help their child learn self discipline

Her diet restrictions are not your responsibility. Period.

Ignore that parent
Not your job to appease her or her daughter

i would take the hint and just stop bringing cupcakes. why wouldn't it be fair to stop making unhealthy food to either tempt people or make them feel obligated to eat. it is a dance school, not a bakery.

i cook for sharing a lot
so not when I do?
I make sure i have SOMETHING
for everyone
gluten free
veg and vegan
and yea low sugar options too, nice piece of fruit maybe

Nor should the others miss out because of one person. If you’re so inclined, possibly bring a healthy snack for that child (perhaps the mother can suggest something, since she certainly wouldn’t want her child’s restrictions to spoil things for the entire group).

If she cant eat one she shouldn't 🤷‍♂️
Doesn't seem like much of a problem to me.

I wouldn't tell a kid they're the only one who can't have a cupcake. That's on the parents.

Put out a plate of carrots.

Sounds like a job for the parent.