All you do is take one hot, the neutral, and the ground. The other hot is not used for a single 120volt circuit.
Two things to look for -- check the generator rating when running 120 volts on just one leg. Some generators will only produce 1/2 the rated output on each leg - so it is possible you only have about 1800 watts available for what you are trying to do.
Second - check, check, check, double check, oh - did I say check
-- all your voltages and connections before you hook up to the camper. If you are not 100% comfortable working with electricity, get help. I have read many horror stories of folks blowing up everything in their camper.
Let us know how it goes!