I would suggest just book the Premier Inn at AUH for them - its landside but attached to the airport and very convenient and quite reasonable.
UAE now gives free transit visa's for 48 hours. There is an Etihad Arrivals lounge after passport control. Prior to departure for LAX, the Etihad Lounge to use is near gate 35.
They will need to clear US immigration and customs in AUH - so allow time for that. There is a small lounge after clearing immigration. Please do not have them spend 21 hours in the lounge. It will be extremely unpleasant.