I'm not torn, as I know whatever is reimbursed by the S corp (and written off by the S corp), can't be also deducted on Schedule A.  I'm just saying that I feel like the child could use the full cost of the property, and take the percentage of that for the S corp to reimburse.

Journal of accountancy seems to suggest that's possible:

 https://www.journalofaccountancy.com/issues/2020/feb/employee-expenses-accountable-plan.html

I was just trying to say that when a home is owned jointly, the joint owners can determine who write off mortgage interest, for example.