If you are talking about insurance for the children, I agree with you -- mom gets to reduce her gross income by the amount of the premium, and dad's child support payment covers his contribution to insurance.
But I think mom is addressing a different issue -- "He is wanting to use the amount he reimburses me
as his insurance payment...." That is, dad is presently still on her insurance policy, and is giving her money toward the premium due to his own continued coverage. While that, also, is likely to end when the divorce is final -- with dad getting COBRA coverage or obtaining his own separate coverage -- as long as he is paying part of the premium in an agreed amount for himself, he has a reasonable statutory argument for deducting that amount from his gross income. In this context, as mom is getting reimbursed by dad for part of the premium, it would be mom who is double dipping by claiming the entire premium as a deduction from her own income while pocketing the reimbursement of dad's payment for his own coverage.
Per statute, "Net income is obtained by subtracting allowable deductions from gross income. Allowable deductions shall include:... (e) Health insurance payments, excluding payments for coverage of the minor child." The statute does not restrict that deduction to insurance paid through payroll deductions.