Paying for ex-husband’s insurance subsidies for shared children?

Short and sweet – my ex husband is responsible for medical insurance for our children; I claim the children on my taxes. He had marketplace insurance last year and did not know or disclose to me information about the insurance. Now, for me to claim the children, I owe in the difference on the subsidies (almost $10k.) Essentially, this is a loan I owe to the IRS; he refuses to get a personal loan to pay me directly this money, and instead wants to pay me every month when my tax payment is due.

This will mess with my tax returns for the foreseeable future, I would assume multiple years through the installment plan. He is legally responsible for medical insurance. What are my options to ensure I am repaid, or that he will get a loan so I can pay the full amount and not have a loan out against me?

I am willing to contact a lawyer, but don’t even know what avenue to go down (family law, tax law, etc.); I also don’t know if the AG can add it to his already high arrears.