Personally I think that this is not a commercial tenancy. Agree with most comments above.
Would add that renting to a tenant who wants to look after the property and may want to stay there on a longer term basis in exchange for less than market rent may still make good business sense so could be commercial.
What concerns me with reference to the Original Post is that if father is also directly supporting the daughter financially with volountary payments as well as charging less rent than they could get which does not even meet the mortgage, than hard to see what is commercial about the overall arrangement. The whole operation appears to be running at a loss.
I think that it would be extremely difficult to go back to terminate HB and raise an overpayment in these circumstancs : My instinct would be to terminate claim from paid up to date. Could now be argued that new information which has not been previously available has emerged to show that not a commercial tenancy.
Regards
Shankers
