Good day to you!
Hope the RV is not spoiling a pretty nice day. But looking at the problem, you've given some very good info and I hate to say but it is quite likely to be worn out batteries on the coach set.
Some things that say that are the weak green light and really low battery voltage. Voltage can be tricking us if we read too soon after there has been any charging going on but when it is that low, it's sure not telling us you have been charging!
One point that often moves me toward checking the batteries is that RV tend to get rundown, either before we get them while they are setting on dealers lots or even after if we don't watch the water in them well enough. The way we use RV is lots harder on a battery than what we see in cars where we drive every few days. Letting them get down too low or stay down too long can damage them.
But let's not jump there just yet?
Taking the RV or batteries to an auto parts store can let them do a "load test" which puts an artificial load on them to see how they hold up. This is often free! Likely you don't want to be lifting them in/out right now!
But first? If you have some type of battery charger, it works best to check the water is good in the batteries and charge them over night or so to help make sure they can do their best.
I go with this first if possible because there are so many things on the RV that require good battery to connect and work right, even though we may be plugged in and the converter is expected to keep things charged. Things like the battery switch have to have power to move the actual relay that makes that connection.
As another way to get some info, if you can start the RV engine, from the start battery not being down, that does possibly tell us some things.
The start battery is NOT charged from being plugged in unless there has been some stuff added to do that charge.
But if that starts the engine, there are several other automatic things that happen if all is well.
There is a connection from the ignition circuits when the engine runs that move a solenoid on older but I think you will have a newer solid state item (that you can't hear!)that connects both battery sets together as well as the engine alternator, so that we get charge from the alternator going to ALL batteries to recharge them.
In theory, we could just run the engine long enough to recharge the coach batteries but it is a 6-8 hour process, so not practical but as a test we can confirm the power from the alternator is getting to the all batteries. If you can test the coach voltage, it will show up quite quickly and that high reading may spook you into thinking the batteries are super good because you may see 13-14 volts really quick! Not true as that is the charge from the alternator and drops off quick if you stop.
But that would tell you that the cables from other parts are getting to the batteries---or NOT if the cables are dirty at some point along the line and need cleaned. If testing there with a meter, test both on the post and the cables and compare to see things are making good contact?
Three year old and down to 4 volts? Sounds suspect but check first. It can be a dirty cable and the charge is getting as close as the clamp on the battery but not INTO the battery? Or maybe there is no water in the thing because we got too busy with other, bigger worries?
My knee rules on some days !