What to do if my boyfriend’s mother is threatening to fight for grandparents rights regarding our 2 month old?

If she says she's going to fight for "grandparents" rights, what she is really saying is that she is fighting for limited visitation access-- not custody. As long as both of you are good parents, married or not, then she can only ask for grandparent access, not for custody of the child.  So your real issue is whether or not you want her to have access and, if so, how do you want her to have that access. 

Kansas does utilize and follow an opionion by the Supreme Court known as Troxel.  Troxel reaffirmed a parents right to raise their child and limit access to a grandparent if the parent felt it was in the best interest of the child.  If you want no or limited access, you need to document and record as many of the odd things she does as you can.  Any threats to harm herself or others can be a valid basis for denying or restricting her access as a grand parent.

You also ask whether or not you would have a stronger case if you were married.  Marriage is not as much of a controlling factors as it used to be... but it doesn't hurt if that's what you want to do.  Marriage should be a choice, not a bargaining chip.  If you work together better unmarried, then stick with that-- because to defend even a grandparent access motion will require the two of you to work together to deal with the stress.  If marriage is in the cards anyhow, it can show a unified front. The main factor, either way, is how the grandmother acts and the threats she has made.  Those are the basis on which the court can deny access... so spend more time focusing on those factors.