I see you have a 2012 Greyhawk. Per Jayco's specification sheet (see link below), you have a generator on board. So you can always run the Genny while you are driving, (nice to have AC when it is really hot), or to recharge the batteries.
Does your MH have the TV located over the cab? You may have a safety feature that keeps the TV from from being powered up while the coach engine is running. If so, remove the outlet for the wall (disconnect all power sources), you will see an extra purple wire, cut it and cap the ends. This wire is 12 volt, to power a relay, that disables the outlet while the engine is running. The ideal is to ensure the driver does not get distracted and start watching the TV.
If you have a good battery bank, you can run an inverter off of it. I bet you already have one, that can powers a few outlets (not all, just a few). Just need to find the switch and then determine what it powers.
You could contact Jayco with your VIN number, and ask for the 12 V DC and 120 V AC wiring diagram. These two documents will show the electrical diagram. It will confirm if you have the purple relay wire, if you have an inverter, and what is connected to it. It might indicate where the inverter on/off switch is located. Others with a MH, should be able to tell you what to look for, in a switch.
https://www.jayco.com/tools/archive/2012-greyhawk-m/
Edit: I see listed in the options a 400 watt inverter.