About 2 seconds after the engine starts, 12 volts gets applied to the Auxiliary Start Relay from the engine. This ties coach and house batteries together so that they all charge. Problem is, the relay made by Trombetta is designed for 12 Volts DC and when 13.4 volts is applied, it gets very hot to the point of discoloring the coil wire. I have talked to Trombetta about this design error in the past but I don't think they have done anything to correct it so far.
The other issue is the contacts. I have had one relay go bad because the contacts burned. I cleaned them and got it working again. Not easy to do since rivets have to be drilled out and replaced with small bolts.
I also modified the coil circuit by adding (I seem to remember) 3 ohms of resistance. This allows the relay to work in its normal voltage range without getting so hot.
After a search, I was unable to determine where your relay is mounted but it's there somewhere. Once you find it, see if 12 volts is being applied with the engine running. If it is, then the house batteries should have the same 13.4 volts that the chassis batteries have. If not, then the contacts of the relay are probably bad. You can either replace it with a new one that you should be able to obtain from a Winnebago dealer or if you would like you can order the standard copper contact or the better silver contact relay direct from Trombetta. Here is the information.
Copper contacts 114-1211-010-03 (Winnie PN)
Silver contacts 114-1200-020 (Trombetta PN)
If there is no voltage with the engine running, then you either have a problem with the Freightliner relay that powers up the Aux. relay or some problem with the wiring. If that is the case, I can only suggest taking it to Freightliner. They have schematics of the chassis wiring that I don't have. If you would like to try tracking it down, there are links to the Winnebago schematics here in this forum. Or you can use this one.