Welcome to iRV2!!
You have come to the friendliest & most helpful RV forum around.
As far as batteries & inverting... that answer would depend on your coach and the year. I did look to see that you have a 2005 Diplomat. I know that Diplomat Don also has a 2005 -and he has put on either the Xantrex Echo-Charge
or the "Trickle-Start". The inverter does NOT keep the engine battery charged on that model year.
I would suggest the Echo-Charge. It seems to be the favorite on this forum.
Again...welcome to iRV2.Please visit & post often.
PS.. I would love to give you some free Monaco karma..
just say "karma please".. and it is yours!!