In this case I think you are looking for a short to ground, because you are loosing both your engine batteries and your house batteries at the same time. This "short" may be discovered in one of your RV solenoids or inside a bad battery cell.
As already recommended, I guess I would also start with what is easiest: A) Solenoid test; or B) Battery Test.
POWER GRID SOLENOIDS
Most RVs have 2 solenoids to manage their 12V power grid, and 1 or both of them is where I would start looking, if you have easy access.
In gas coaches these solenoids are often located under the front steps or near the batteries. In diesel coaches, like mine, these solenoids are located behind a cover in the inverter bay.
The solenoid that fails most often is the battery disconnect solenoid.
All coaches have a battery disconnect solenoid (The Salesman Switch), and if your coach has a "Battery Boost" switch, usually located in arms reach of your driver's seat, then you know you have second solenoid too.
Most people will just replace their the battery disconnect solenoid (no test) with this one by Intellitec, but your coach may have a different configuration:
https://www.amazon.com/INTELLITEC-01...2109325&sr=8-2
HOUSE BATTERY TEST
Two plus year old house batteries are always suspect and 90% of the time this is your problem. (Shorts are easily found. Sulfated batteries no so much!)
...And coaches with only 2 house batteries fail sooner than 3 or 4-battery 12V systems, because the 2 volt bank with less Amp-Hour (AH) of storage usually forces the owner to draw down the battery bank SOC to below 40% in between charges.
...And house batteries that are not the deep cycle type will often not last more than 1-year.
...And batteries stored in freezing climates without a battery maintainer will also not give you the useful life you hoped.
..And sealed-lead-acid engine batteries don't fail as often as your wet-lead-acid (deep cycle) house batteries.
...And if you are not fully charging your house batteries in between use then this will result in shorter battery life.
In this case, if one of your house batteries has a short in one of the cells that could be your problem too.
* Take your fully charged house batteries to a Les Schwab or Interstate Battery or Napa store and they will l test your batteries with a Load Device for batteries. (80% of the time this is an accurate test, however, these load devices are made for engine-start-batteries and sometime will "pass" a bad deep cycle house battery.)
* This summer my 2.5 year old (4-GC2-Golf Cart) house batteries were passing the load test and passing the hydrometer test, but over the course of 2 weeks, on inverter power... I would watch my EMS voltmeter show 12.7V and then drop to 10.8V in 3 hours, then 2 hour, then 30 minutes, which is a classic symptom of a single or multiple bad battery...
...But I refused to accept it was a house battery problem because I really worked hard to treat my house batteries right. So I kept thinking my inverter was shorting internally. ...NOPE! ...It was my house batteries. I.e., in my case my house batteries probably got badly sulfated. ...But my engine batteries were fine.
If your engine batteries is are loosing there charge (before your house batteries on a relative scale) then you might have a bad alternator. Or to be more specific the diodes inside your alternator are shorting to ground. And since you cannot replace these diodes, the remedy is to replace your alternator. However, I doubt this is your problem, because you would see a dash light coming on.
ALTERNATOR TEST
A fully fully charged 12v battery will read 12.7V, so if your voltmeter is reading above 13V at your engine battery or house battery, then you know your alternator is charging.
Linear Mode
