Some suggestions and some questions to clear what the situation might be?
For best understanding of what to expect, did you get a big folder of info with lots of manuals for the RV? If so, doing a look there on what to expect on the inverter will be a good start. Not always the most complete and many things not clear but a general good place to start.
If not on hand/missing a look online for the owners manual is needed as a starter and maybe a place to find out how much one DOES NOT know about a new RV. It's normal!
The problem is that things keep changing and every RV is a bit different, so the manual is looked at as a start for many.
Then on the electrical questions, is this a DIY (if possible) or looking for places to referr others to for fix?
If going DIY, knowing exactly which serial number to look at is good, just to avoid confusion, but there are some basic things that could be checked if you are set up with a meter to test voltage.
When not having a shore power connection for full 30 amp service, I would start with making sure you are getting full service from the generator by checking at the transfer switch.
Looking at this drawing, the idea is that the cord or the genrator will both provide the same power when the cord is plugged to the right full power and then the transfer switch chooses which to use, cord or gen. and passed that through and on to other equipment.
I would first want to check the two connections at the transfer switch with the generator running to see 110AC at both connections as it leaves the switch.
I'm not familiar with the EMS module, etc but looking at this drawing, I do not feel either washer will involve the inverter, so on or off is not a factor.
That is open to change if others who know this system say different!