They arrive at 22.35 and depart at 08.00 so say 9 1/2 hours of time
Allow at least 30 mins to clear the CBP and collect bags and to have checked in an hour before the flight the next morning then they don't have a lot of time faffing about trying to get to an off site hotel so they then have 8 hours which includes gettign to and from the hotel so even less time to rest than that,
Whilst the TWA hotel isn't perfect in this case it will likely suit OPs Family members and their kids who will no doubt be tired and need a bed asap. If they were arriving earlier or departing later so had more time then yes an off airport hotel might indeed be better
As to estimated tax costs uber as a fare estimator tool on it's website.