If I'm leaving my husband and moving to another state with my children, what are my legal rights to keep custody of them?

I would retain an attorney as soon as you can and speak with him or her about your intentions to leave the state.  I would caution you against doing same unless he consents or a court allows you to in an order. Otherwise you could be considered kidnapping them.  You have the same rights as he - so you can not take them away from him unless the court thinks it is in their best interests. Good luck.