RVer402...it isn't fun figuring it all out but rewarding when you do.
I think you need to separate these 2 issues. The EMS is separate from the inverter. They may appear interrelated but except under strange situations they are not probably related. I'm only going to deal with the inverter because this will be a long message.
At the outset let's just clarify that your water heater, AC circuits 1 & 2, washer/dryer and dishwasher/fireplace are NOT inverted and do not pass through the inverter. This applies to any outlet that you find that doesn't work on the inverter.
The first thing I suggest you do to get this sorted out is to determine what outlets are inverted and what circuit they belong to. This is pretty easy to do but a bit tedious. The one circuit you do know already is your microwave and unless you can access its plug you shouldn't have any possibility of extra loads on it.
This is the tedious part but it can be very instructive on your integration of inverted (battery powered circuits) from those that are non-inverted (the rest).
1. Unplug everything you can reach from every outlet. Except leave your microwave and refrigerator plugged in.
2. Go to your inverter sub panel and turn off every breaker except SUB MAIN.
3. Disconnect from shore power but leave inverter on.
4. Now, turn on the microwave breaker and run it for a very short few seconds to validate it is running and not popping anything. Take notes and turn off breaker.
5. Repeat step 4 for for the refrigerator and if there is a vacuum test it too and turn off breaker when done. (Is it a residential refer?)
6. Turn on RECPS 1 and use either a plug testing device or a small 120V plug in device (like a small lamp) to test all outlets in coach. Any outlets you find that work are inverted on that breaker so use some labels to mark these outlets as R1 (short for RECPS 1). Turn off breaker.
7. Repeat step 6 for RECPS 2 except you can skip any "R1" outlets. Label breakers that work as R2 then turn off breaker.
8. Repeat step 6 for RECPS 3 except you can skip any "R1" & "R2" outlets. Label breakers that work as R3 then turn off breaker.
All other outlets that don't work are NOT inverted. You might label them as "NI" (not inverted) for now.
Hopefully you won't have any inverter problems if you do it this way. If you do have problems then it is likely that your inverter is having some kind of problem.
The combination of plugs labeled R1, R2 & R3 along with Microwave and Refrig/vacuum are all the circuits and plugs that are on your inverter. The combination of all these circuits can never exceed your inverter's (2000W?) rating except for some surge within your inverter's capabilities while on battery power. If on shore power you can not exceed 3600W (30 amps) and it is possible that you won't have much if any "surge" protection about that.
If at this point you haven't seen any problems you can start turning your breakers on starting with your refrig and microwave. I would run another test with both of these on at the same time to see what happens.
Now, go ahead and turn on RECPS 1 breaker and plug in anything that was in those outlets before you started this testing.
Repeat for RECPS 2 & 3.
If all is good you could again turn on the microwave. If it pops the inverter reset then you know that the microwave in combination with other devices is too much for your inverter on battery power. You will need to adjust accordingly.
Unfortunately, with a 2000W inverter you will have limited options on what you can run while on batteries. I am highly interested in how much power your refer and microwave can draw. What models of these do you have? It is highly possible that having a TV on and the refer cooling that the microwave (or any other high power device) could be a tipping point.
Now that you have completed all of this you should have all sub panel breakers on and you can return to shore power. Since everything was plugged back in by now, test the microwave again to see if it pops anything and take notes.
With all the labels and notes you can start to put together a picture of how much your inverter can do. It isn't fun but could help in the long run.
Keep in mind that the total power of any "R" circuit can not exceed 15A each. On top of that when on battery power the total power of all inverted circuits can not exceed about 18A and when on shore power 30A.
I know this sounds complicated and it can be if you don't have confidence in your ability to juggle all these numbers. Just take your time. Hopefully my suggestion make sense and will help you separate out inverter problems from EMS issues.
Sorry if this is too much information and it causes your eyes to roll to the back of your head.
Just take your time.