Ok, Electrical 1.01
The way those testers work is they look to see where there is , and where therre is not. voltage.. You should have 120 volts from HOT to Neutral, and from HOT to Ground.. and zero from neutral to ground
In an RV the ground is indeed floating, and if you are using a generator to power the RV odds are very good it is not grounded.. THUS you can get some real strange readings on those 3 light testers.
Now, when on SHORE power, you have one pin on the plug that is kind of round, (may be U or D shaped but kind of round) and the other pins are FLAT.
That different pin.. that is the ground
It is SUPPOSED to be connected to the neutral at the service entrance (That is the main park distribution panel) but in many parks.. it might not be.
And of course there is always the posibility of a broken wire, or bad connection within your RV...
Suggestion>> Find out which.