Wow.
Maybe you can't afford $50 once a year for his birthday, but I am guessing you probably can.
So why not be the bigger person and pay the whole bill to keep your son happy?
Sounds like the lady was an annoying old hen and I understand your desire to stick it to her, even still ...
Birthday is once a year, what will your son remember, a fun party or a drama over the bill?
I guess it's "the principle of the thing".