The main issue here is OP was TOLD that he is all set that his family members could stay using his points. From the hotel's point of view - someone attempted to check-in to a reservation that was made from and by another person. How could a hotel know that the person showed up was OP's family member?

It's the "I was told" without any proof situation.

The same thing happened to us a few years back - Mr made a reservation and he arrived later than us. Me and the kids wanted to check-in before him so that we could leave our stuff and drove to the airport to pick him up later in the day. I called Marriott and they assured me that everything was in order. Guess what? We got there at the check-in time and FDC said I'm not xxx and if xxx is not here you can't check-in. I used the "I called Marriott and they said it was all set" thing to the hotel and FDC still said no. More conversation back and forth and she finally agreed that I had to drag Mr to the front desk with his ID after picking him up from the airport - if he didn't show up they will charge me CC in full for the stay (I let her authorize my card). It was a total ordeal. Lesson learned, always document everything.

This was before the app works - if we run into the situation again I'll see if I can chat with the hotel before.