I had a crazy running 1988 BMW that was fine after I replaced the battery the second time. Yes it did not run right with the old battery or the first new one but did with the second new one and both were from WM.
I have three 12v battery under the nose and can just rob a house battery in a couple minutes by changing battery connections. Not sure about your set up. If our key is on the chassis and both house batteries are in parallel so when our alternator was out I kept the house battery next to the starting battery disconnected so if we lost the generator we could get off the road if the other two batteries died or shorted out.
Have you had the house generator running any while it was missing? Do you get any back firing?