It sure sounds like your battery is not connected to the RVs 12V system. I am not sure where you measures the 11.5V after disconnecting from the truck (by the way, don't expect the truck to significantly charge the RV battery) and the 12.8-13 when connected to shore power.
It could be the batteries are shot and won't hold a charge. The converter will produce around 13.5V on shore power so 12.8-13 seems low.
Hopefully you can use a VOM. If so, it is relatively easy to follow the 12V wiring to find where the problem lies.
Thanks to Daryles, here is a link to the diagnosis flowchart. Refer to Post #3 in the Thread
https://www.montanaowners.com/forums...ad.php?t=86323