I see a lot of folks suspecting GFCI's... On circuits which often do not have GFCI protection..
That said, I have heard of an RV Fridge being on the GFCI loop, no reason a MIcrowave can not be put on one too even if there is absolutly no reason to do it with either of them (easier to properly ground them and let the circuit breaker do it
Power to a 50 amp rig comes in on 3 wires, Two hots and a neutral, it matters not if you are plugged into 20, 30 or 50 amp there are two hots and a neutral, the adapter for 20 or 30 feeds the hot wire to both hots. If you have an automatic transfer switch and ONE relay is hung, that can do it,, Since the problem exists on both Generator and shore power I'm guessing the power cord and inlet re good.. the Transfer switch is not suspect #1 but the first suspect in the line
Then we have the wires from there to the MAIN brekers, the Main breaker, and finally the branch breakers and the wires to the devices,, This includes the outlet
The fridge is the easiest to check
If you step outside to the fridge's back door and open it you should see a 120 volt outlet and plug.. (Though that is the normal spot they sometimes put them elsewhere just so you know) Unplug here and plug in a lamp or fan.. Make sure the lamp or fan or test light is turned on.. LIGHT is good, Dark is bad (or wind good, deadl air bad)
Then get back with us.
Oh, the breaker box (Mentioned earlier) with no power (unplug, generator off) make sure all the assorted screws are tight... Many rvers have a few screws loose, often in this area.