I will admit that the quality of the beach at RP is not great. But there is a lot of room and several shade palapas, so it is easy to spread out. Roxxy is gone, so you don't need to worry about that. I can't remember which side of the resort it is for sure, but I think the side of the resort that is closest to the bridge does not have any noise problems regardless, from other places.
Frankly, I think the problem for you is going to be that the quality of RP as a resort versus Belair, is in a whole nother universe. Regardless of fixing the a/c problems, I think your family may not want to go back to Belair after being at RP.