son will not get even a bit sick from *not eating dessert*, for daughter's birthday she deserves her choice of treat (within availability and budget constraints), son needs to have a meal he will eat and not go hungry, but daughter should not be taught that her desires are secondary to her brother's even on her birthday.

If you want to cook a chocolate cake because you enjoy it, do it on your own time. If you can't make cheesecake I am sure they can be bought. If they are unaffordable, that is a different problem.