Thank you for the pointers. Yes, there is advance Premium Tax Credit and Father (being the lower income earner) is getting a few thousand $ refund because of PTC. I think I should get Mother to sign a doc attached to both Father and Mother Tax Returns to the effect that Father will take 100% PTC Allocation for Credit.  Father is asking, if he should get Mother to pay for the daughter's share of health insurance cost? So inistead of Mother Paying for daughter's premium, perhaps Mother can just have 0% claim to PTC.  

Yes, due to her higher income, she would have to pay back the PTC for her daughter.