Hi, TexasGal! The Avenue is something we all probably know a bit less about - I didn't even know there was such a thing until I spotted one on the road near my house a few months ago (URL here for those who are not familiar with it... Air Forums is having itself a cranky Monday morning right now and will not allow photo attachments).
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A few questions might help get your issues constrained:
-- One or two house batteries?
-- Do you have a digital battery monitor or a generic red/green bar indicator of the type Airstream typically installs?
-- Have you changed out the battery(ies) since buying your Avenue? Do you know anything of their history? Age? How the previous owners stored the vehicle?
-- Can you access the battery to examine it? Whenever I hear allegations of "my house battery is always low", the first thing I wonder about is possible damage due to historical mis-use. You can see from a few other threads on here that we talk about battery "bulging". You will want to check and see if that is the case with yours. Or even if it is a Lifeline battery to start with. We bought a used Airstream Interstate and we faced this issue at the point of sale. Our seller wanted to change out our previous-owner-damaged coach battery for us and put in something cheaper than a Lifeline. We said no and negotiated for a Lifeline. If the wrong battery got put in your Avenue prior to the sale to you, it could be an issue.
The general logic in a situation like this is, first establish that the battery itself is OK. Then once you have confirmed that you are working with viable equipment, move on to troubleshoot procedural factors of the situation.