Primary residence is deeded in both names but mortgage is only in mine. I want a divorce but my husband does not and states he will not move out. Do I have any leverage being the mortgage holder to be able to stay in the house with the kids during a seperation and after property division?
No, unfortunately your having all the liability on the property does not give you any greater right to possession than he has.
So what happens if I move out? Who is responsible for payments on house, utilities, etc.? Is this something that would be decided between us and put into a Separation Agreement?
Yes, if you can agree to a solution, otherwise, you are ultimately responsible for the mortgage.