As pointed out, the GFCI outlet in the bathroom will not reset until good power is restored to it. So, at this point it is safe to assume that 110 vac is not making it into your camper.
The first thing to do is ensure that power is being supplied at the outlet you are plugged into. I assume you are plugging into a regular 110 v wall outlet on the outside of your house, so try plugging a table lamp into that outlet to make sure it is actually working.
It's pretty much impossible to test anything beyond that without at least a multimeter. However, you can try resetting the main breaker on the breaker panel. That is, actually turning it off and turning it on.
The problem could be in your dogbone, or it could be where the camper's power cord attaches to the camper.
Did the air conditioner work when you picked the unit up from the dealer?
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