"- Father will hold the Mortgage, Kids will hold the house title"
This part won't work. At least one borrower must be on the title deed to qualify for a mortgage loan. However, most mortgage lenders prefer that all borrowers appear on the title.
VA loans also have occupancy requirements:
https://www.veteransunited.com/valoans/occupancy-requirements-for-va-loans/Here are some risks/concerns:
1. Children are habitually late paying the mortgage, and it reduces Dad's good credit.
2. Children stop paying property taxes, and the property is foreclosed on tax sale.
3. One year comes up, and refinancing rates are significantly higher than the 4% of the kid's previous loan, restricting the Dad's ability to get out. (not unrealistic since 1 year is not very long to rebuild kids credit)
4. Dad wants to buy a summer home, but cannot because the outstanding mortgage debt it too high for his income.
5. Kids standard of living increases by the amount of the monthly savings, so that even though the mortgage payment is not as high, other monthly payments have filled the gap, and kids fail to pay down their high interest debts.
6. Kids stop taking care of the house to the point where it requires so many repairs, it makes financial sense to offer up a deed in lieu of payment on the mortgage - makes financial sense for the kids, but not the dad.
7. Dad's health declines, and, because he holds the mortgage on the house, feels entitled to occupy the house and sell his own house.
The better solution would be a loan from Dad to pay off the high interest debt, with the loan recorded as a lien on the house. I suspect this isn't workable due to Dad not having the cash the fund the loan. It would be cheaper for Dad to gift kids the difference between the current mortgage payment and the new mortgage payment, than for him to be on the hook for the entirety of the new mortgage payment.