Legal Question in Family Law in Kentucky

This isn't a legal question, because there isn't a legal problem here for you. The birth mother has no parental rights; at the point you adopted the child, the birth mother's parental rights were terminated. If you don't want your daughter to have contact with her birth mother, then you have the right to tell this woman to back off and leave your daughter alone. If your daughter wants to have a relationship with her when she's 18, then that will be her choice. Until then, it's your choice.

For this woman to contact your daughter on Facebook was incredibly inappropriate, but what happens next is entirely up to you. If you believe it is in your daughter's best interests to have a relationship with her birth mother and birth siblings, then the choice is yours. If not, take a firm stance with her. Regardless, I would suggest talking to a family counselor about the situation, and also having your daughter speak with a counselor. Immediately.