I am a member of the State Bar of California, the Bar of the U.S. District Court for the Central District of California (San Luis Obispo, Santa Barbara, Ventura, Los Angeles, Orange, San Bernardino, Riverside Counties), and I have comprehensive knowledge of California family law.
Your ex can ask California Department of Child Support Services (DCSS) to assist in coordinating your arrears obligation with the NJ Administrative Office of the Courts (AOC). However, this is not actually reopening the case -- it's just collecting the unpaid balance of support.
California has no jurisdiction to establish a new child support order, and even if it did, California law provides that child support terminates at age 18 and graduated high school, or age 19, whichever occurs first. Consequently, DCSS would reject any attempt to order additional support for your ex or the adult children.
I hope I've answered your question. Please let me know if you require further clarification. And, please provide a positive feedback rating for my answer (click 3, 4 or 5 stars) -- otherwise, I receive nothing for my efforts in your behalf.
Thanks again for using Justanswer!