Get a battery operated CO detector and use the furnace.
Actually in a 30 year old trailer get a new propane/CO combination detector, a new CO detector and a new smoke detector.
Still 50 degrees should be perfect for no heat needed. Even an extra blanket could have those little ones overheated.
Oh for the excitement to be a parent for the first time again... don't forget to have fun! Take lots of pictures. We started an RV travel log notebook with DD first trip that has a short story for every camp trip. Really enjoy looking back sometimes.