Welcome to forum Tinman
Coach battery not the chassis battery right? First thing I'd check is to make sure the Tripp Lite inverter/charger is set to "charge only" when you are not using the inverter. Roadtrek started using that inverter in 2004 so I am assuming your RT has it.
This topic: http://www.classbforum.com/phpBB2/vi....php?f=12&t=20
shows how to make a remote switch for that inverter.
The second thing I'd check is to make sure no lights were accidentally left on in the "trunk" or in a storage compartment.