It is your obligation to invite both parents. Having said that you must tell both parents that you are inviting both to the party and it is in the children’s best interest that they both come and behave themselves. IF THEY feel that they can’t do that then they should decide to take turns and choose which one will come to this simcha and which one will take the next turn to come to the next one because you will keep telling your children to invite both their grandparents always and to love ALL their grandparents the same.
Let them each know that it is not YOUR job to be the referee between them and you have no intention of being pulled into their nonsense. Just as you teach your children to stay out of it, you are choosing to stay out of it as well. It is THEIR problem not yours. YOUR issue and obligation is to keep shalom bayis and peace in YOUR family and in your HOME. THAT is what YOU must teach YOUR OWN CHILDREN.