Unless the conduct of the other parent is extreme in terms of violence and is supported by evidence, a limit at the beginning of a divorce proceeding, generally will not allow you to move and will likely order the return of the children to the marital residence pending a final Court order or agreement by the parties.
Once you have appeared in the divorce proceeding, you can then ask the Court for permission to move with the children. In order to succeed, you will have to establish that it is in their best interests to move. You will have to explain why you want to move, why it would be better for the children, how you intend to deal with their relationship with the other parent, and so on.
It is very important to show where the children will be living, where they will go to school (including how the school is rated), what the area is like, whether there is family to help with them, whether you will be employed, and how your ability to support the children will be affected. Pictures are worth a thousand words, so it would be wise to show pictures of the home, the school, the area, the parks where you will be living, etc. If you don’t have the evidence, the Court cannot really picture what things will be like in the new area, and you will be likely to fail in your request.
Relocation separates the children from the other parent geographically, so it is very important to show that you will encourage contact as frequently as possible, including significant time during school recess periods and the summer. Also, willingness to contribute to travel expenses or take less child support, if possible, would be a plus.