This may be one of the most misunderstood of all parts of an RV!
On the RV I have had, they have all had this method for coach and chassis batteries.
When the engine is running, there is a solenoid which pull and connects the two battery strings together and that lets them both charge. Like after a long weekend and driving home or to the next site, the coach batteries get some charge back. Full charge if you drive far enough.
But when you shut the engine off, they do not want you using the coach items and running both sets of batteries down, so that you are dead all around when you want to leave. To avoid that, the solenoid I mention does not stay pulled when the engine is off and then you have two separate strings and the coach is charged from shore power or generator but not the chassis battery!
There is often a switch near the driver which does connect chassis and coach battery together to let you "cheat" a bit to get the engine started if that battery is dead and the coach has some left.
So when not pressing the button, norengine running the battery strings are separate. One result that we often read about is folks store the RV plugged in but come back and it won't start because most vehicles have some "parasitic drain" like radios, clocks, etc.
But the best solution I've found is a small system called Trik-l -start
https://www.lslproducts.net/TLSPage.html
Shop for best price but very easy to install DIY with only three wires, one to coach battery, one to chassis battery and one to ground. Then it is all auto stealing just a bit at the right time to keep the start bat up.
Rereading makes me wonder if I get the piture right. Are you saying ALL batteries are dead? That would need a look at the converter, not inverter, as the converter changes the incoming 110 AC to 12VDC to charge batteries. It will not charge the start battery, however.