Custodial Parent Rights

My daughter has primary custody of her and her ex-husband's two children (ages 7 & 8). Her ex-husband is a member of the U. S. Air Force and stationed in New Jersey. My daughter has remarried. Her new husband is employed, my daughter is in the process of qualifying for SSI disability. Her ex husband sent her a text message stating that he was willing to give up custody of the kids.

My question is:

If my ex son-in-law gives up custody of the kids, does he also relinquish his responsibilities for providing them military health care and financial support as well as educational expenses, medical co-pays, etc.

Thank you for your help.

Rella