If your RV has a Bi-Directional Isolator Relay Delay (B.I.R.D.) it disconnects the house and chassis battery groups until a charging voltage (+13.7v) is detected. Your description shows your isolation relay isn't working in both directions. I suggest you search your electrical bay and see what you do have and then use Google to search for that unit and then folks on here can help you test it and suggest solutions.
makes many types of modules, perhaps you have one.