Can my ex mother in law demand a paternity test for my baby and can I sue her for defamation of character?

I am 8 months pregnant and no longer with the father of my child. I found out that his mother is accusing me of sleeping around and she is also saying that my ex is not the biological father of my baby. I have nothing to hide and I know who my baby's dad is, but he doesn't have a backbone and does everything his mother tells him. What can I do?