Something else to consider from the inverter side of this...
You have a '94 RV with a 2001 inverter and have owned it for 2 years.
How much did the previous owner use the inverter, and how many times has it tripped before you owned it?
I don't care how well built or installed something is, it will only trip into safety shut-down so many times before the circuitry begins to fail. When it does, it could either trip for no real reason, or fail to trip. Yours appears to be all too willing to shut down. I would contact the manufacturer to see if they might be able to test/repair it or find an electronic repair person with a shop who can diagnose component level failures. Perhaps the manufacturer can refer if they don't care to do the work.
I have repaired a few inverters ranging from dinky 75W units up to the 1500W I am currently using in my rig. If you're lucky, you have a unit failing due to bulging capacitors. Many electronic devices made around the vintage of your inverter had defective capacitors installed during the manufacturing process. These capacitors have a tell-tale sign they are failing since the tops bulge up. Simply replacing them can restore your electronic device to working order. They are usually a cheap component as well, so a decently qualified shop can handle the job IF that applies to your inverter.
If you can easily access the unit and peek into it through the openings for air flow, shine a flashlight into it and see if the top of the electrolytic caps are flat. A quick google search for "bulging capacitors" should return all the help you need identifying them ans determining if they need replaced.
The bad capacitors were used in a very wide assortment of electronics so nothing is exempt from this possibility. Computers, monitors, radios, TV's, ect...
As with anything electric related, make sure the POWER IS OFF and ALL CIRCUITS ARE DEAD before touching anything. Unplug from shore power and make sure the generator is off.
If you are unsure about doing the inspection, just about any electronics technician can do it for you.
Joe