I don't think you over reacted. I also think you need to talk to your cousin or this will grow into something that could cause you two not being friends anymore.
I think the 2 year old needed DISCIPLINE, she need to be taught how to act around small animals. The 2 year old did not really know what she did was wrong, they really don't have empathy at that age and it is up to her mom to teach her what is acceptable. 2 year olds also imitate what they see around them... that makes you think!!!
As to crating or separating your baby, it is better than her being hurt again. If she nips your cousins baby the cousin will be all mad and blame you.. without thinking why she nipped. So for now, the 2 year old and your baby do not need to be together without you there.... period
imo
Good luck, keep us posted