I think your idea of spending NYE together in the hotel room sound absolutely wonderful, I would have been kicking off hugely if all the family invited themselves to my intimate little night away and ruined it like that. As for the listening service, my thought was 'how do they do that?', if its monitors, your baby is awake and crying it's eyes out before anyone reaches it, and some 'listening services' involve someone going and checking on babies/toodlers every 25 minutes to half an hour, meaning potentially, baby could be left alone for over half a hour awake and crying........no way!
My FiL has stayed in hotels so small (guesthouses really) that you could use your own monitor and be there before baby is even properly awake, and when there is only a dozen other rooms, that isn't a issue, but in a full size hotel, I wouldn't even think of that option either, as one of the other ladies said, what if there was a fire?