Wow. I would explain that since you are no longer attached to STBX, his entertainment expenses are not your concern. Furthermore, when he has custody of the child at any given time, you are neither in charge of or nor responsible for their plans or the associated costs. That's sort of fundamental to how divorce works, really.
I am flabbergasted that there are adults who think it would be reasonable for an ex to pay entrance for STBX and baby to get into a waterpark during STBX's custody time. Do they think he is just a glorified babysitter? That's his kid, his custody, HIS financial responsibility.