The court will always have jurisdiction over the issue of child support, visitation and custody as it is to protect the children. It is a possibility but as the years pass it is less and less a possibility.
My name is Stephen R. Cohen and have practiced since 1974. I practice in Los Angeles and Orange County, CA. These answers do not create an attorney client relationship. My answers may offend I believe in telling the truth, I use common sense as well as the law. Other state's laws may differ.. There are a lot of really good attorneys on this site, I will do limited appearances which are preparation of court documents it is , less expensive. However generally I believe an attorney is better than none, but many will offer a free consultation and a face to face meeting generally will be better, I like my clients to write a short one page history of the fact and questions they have prior to meeting with them, so nothing is forgotten.
This seems quit dysfunctional. Yes, "IF [you] moved closer could he then file to restrict our movement in a way it is not now" and he can do if you don't move closer.
Unless he has returned to the workforce you have little to gain with your support motion except an order requiring him to make contacts in the Greater Depression. I would utilize the Co. Dep. of Child Support Services to pursue any support motion.