WOW. I mean... just... WOW. I am appalled at this woman's behavior.
I REALLY like Mary K's take on this - but - I would make your response shorter, crisper, and more succinct. My experience with people like your cousin, is, the more words you give to somebody who behaves this way the more it validates their bad behavior - and allows that person to think he or she can walk all over you. How you handle this, will determine how she behaves towards you in the future. Nip this in the bud.
I would not worry about any family awkwardness on your part, because I'm pretty sure she's already annoyed plenty of people in your family. This kind of behavior isn't a one-time thing.
And seriously, you have a family to love and care for. Why should you blow your budget on someone like this?
I am genuinely shocked at how she handled the topic of children. If you are planning and event, and don't want small children there, why not just say so?
She sounds very passive-aggressive and manipulative.