The main breaker keeps tripping. The outlets will work with…

Have to check everything that is on that circuit for that breaker. IF you had a loose or wires touching at one of the outlets then it can cause this type of issue. I might isolate the AC power and check all the outlets that are going down when the breaker trips. See if the fridge and water heater are tied into that breaker as well. I have seen some cases where an AC heating element on the water heater or fridge shorts out and can cause this type of problem.

The inverter is also suspect if the main breaker is tripping, the inverter takes the battery voltage and makes the AC voltage however that voltage passes through the inverter then to the breaker panel so if the inverter or batteries were in bad condition then it might cause the breaker to trip. The inverter will charge the batteries when plugged in and if the batteries are depleted or in bad condition it would be an issue so I might have them load tested.

When you are plugged in the inverter should not be inverting if that was the case it would try and pull from the batteries and try to charge them at the same time.

The incoming AC voltage will go through a transfer switch as well so you may want to inspect the transfer switch wiring and make sure no wire are melted or loose.

My feelings are if it is the main breaker tripping it is the supply, transfer switch or the inverter.

You may want to see if a mobile RV tech is in the area that can come to you, normally if you do an online search RV mobile repair and the zip code the RV is at you should get a listing of techs, a problem like this can get complex and not sure how much more I can assist you on this site without being there in person. 
Robert

Both the shore line and generator line go directly to the transfer switch, could be in a box next to the shore cord, some older Country Coaches it was in the bedroom under the bed or in a really small cabinet next to the bed, the bottom false bottom comes out and will expose it very hard to access if it is in that cabinet.

Might want to locate the water heater and disconnect the AC wiring to the heating element and see if the problem continues, these older water heaters are wired in a way where they are wired direct from the breaker panel. The AC heating element would be opposite of the outside access panel, that may or may not be the issue, I have seen the elements fail and trip the main breaker as it creates a dead short.

Have to try your best to isolate whatever is on that main breaker or the breaker that trips, Shut all the breakers off as well and turn the main breaker on first, if it holds start turning the others on and see when the breaker trips then check what is on the breaker for what caused the main to trip.

Robert