I know that you are hurt by this and your feelings are warrented, but know that you could never be replaced. In some cultures all caregivers are known as mommy, but the children will always know who their "MOMMY" is. I wouldn't worry so much about it, especially since she is not there 24/7 but only part time. My daughter is two as well and is still working on her language skills. Your two year old may equate the word mommy with anyone who takes care of him.
Your cousin probably feels so honored that your child calls her mommy, however if you've asked her to stop then I think she could honor your request. Perhaps ask her to make up a name that only your child and her could use...like mimi or aunti...or something. I would be hesitant to correct in front of your child, but to address the situation when the children are away so as to not upset the two year old. I would hate to lose a great caregiver over an issue like this because it isn't as if she is hurting the child. But any childcare giver should honor your feelings. Talk to your husband too and atleast let him know of the situation so that it doesn't cause a big blow up on his side of the family. Maybe he can give you some insight as well on the family back ground. (although if he is anything like my husband, he will not think anything is as big of a deal as it is!) :)