Given that the OP's adult child needs to stay in the same room and the huge difference in points the OP needs to pay for a room that can accommodate three adults (compared to the points required for a standard room that can accommodate two) at most hotels, I would suggest looking into some of the Residence Inns in London as some rooms have a double bed + sofa bed and don't require additional points. I would also suggest contacting hotels that have rooms that can accommodate 3 adults directly and asking them how much cash you would need to pay to upgrade from a standard room paid with points to the larger room. Frequently, the cash difference as a percentage of the cash cost of the standard room is substantially less than the points difference as a percentage of the points for a standard room.