My husband wants to move out of my parents house as he does not get along with my mother, but I want to stay with my parents. What should I do? He had agreed to stay with us but now he is not..

As a family, i guess everyone can sit down and have a talk to address the issues. Otherwise you may ask him whats the issue and find a time to talk about it with your mom. Try to work things out. Alternatively, move out to somewhere near. So its easy for you to go back home. And he still has his own space.