You have proper voltage out of the converter (What model please) to the house. but low (Battery) voltage on the USE/STORE switch (Also what model if you can tell me)
Suspicion is: Defective USE/STORE switch and/or Battery disconnect solenoid (#1 in my book is the switch)
#2 suspect is a pair of circuit breakers
My coach, and I kind of suspect yours, has an Intelletec Battery Control System under the hood (yours may be elsewehere) this is a big black box that says "Battery control system" on the cover. Now, I will tell you how MY house is wired
THe converter feeds the fuse panel that feeds most everything, including the volt meter in the BCC's remote panel.
The schematic for the BCC shows two post type 30 amp breakers (Push to reset) in the bottom of the box.. I do not have those, I have a self-resetting breaker (bigger) next to it, but if those breakers have "Tripped" then there is no connection to the house batteries A RESET will fix
IN my case the switch failed.. Oh, "Disconnect" (STORE) worked fine, but "USE" (Connect) no joy.. I will tell you how I fixed it.
To test this you need a bit of quiet and may need a partner depending on where the box is.. Press the switch you should hear a CLUNK, if you don't press "STORE" if you now hear a CLUNK you found it, the problem.
If you do hear a clunk both ways move to the location of the clunk (That's the BCC)
Mine has 3 heavy duty cables, and connections
1: Generator (house)
2: Chassis (I think) or Main
3: AUX (House battery)
Use a volt meter to measure between each of those 3 and chassis ground.. You should see
Generator: Proper 13 volts
Other two, Low voltage
Jumper Generator to AUX.. Hopefully you won't need to also jumper in Main.
Now, back to fixing the switch
Remove the panel from the wall, disconnect the plug on the back, operate the switch 50 to 100 times, both sides, re-connect and try again.. CLUNK/CLUNK (use/store) you fixed it
Switch is self cleaning, and that's how you self clean it.
Home is where I park it!