Yes, Airstreams are nice quality units, but the OP just had a few battery storage questions.
Captain, to keep it simple:
1) I would disconnect the coach house battery ground while the RV is in storage (you can leave the disconnect switch on). This will prevent battery drain and should be OK for a month at a time. I use a stainless steel wing nut on the battery ground to make it easy to disconnect - no tools needed. Tractor Supply has them.
2) Then on your visit to the storage site, re-connect the ground to the batteries and plug in the coach and the onboard system should charge it.
3) When charging the house batteries, use a voltmeter to check the chassis/engine battery. If it is 13V or more it is charging. If it is 12V or so, it is not. If not and about 12V, carefully jumper the + Chassis to the + House batteries and they will all charge together. You want to be safe here because any + to any ground will ruin your day.
Tom and Amy from Northern Virginia.
2000 Allegro 454/Workhorse P32/TST/Crossfire
Life is a DIY project - enjoy it.