DO NOT TURN IT ON while connected to 220. You will regret it. Don't try to understand electricity, just respect it and follow the rules. It is confusing and deadly. This is what you need... It sounds like you have the correct plug as you stated you purchased the RV box from Lowe's. What you need now is to purchase a "Single Pole, 120V, 30 amp breaker" (I had to get my GE brand at HD as Lowe's did not carry it. They do carry Square D and Westinghouse)and some #10 2-wire with ground Romex. (It will have orange sheathing).
This is how you connect it. In the Service Box (Breaker Box) connect the BLACK wire to the breaker you just purchased, connect the WHITE wire to the NEUTRAL BAR, connect the BARE wire to the GROUND Bar. Now at the RV box connect the BLACK to the Brass connector, the WHITE to the Silver connector, and the Bare wire to the Green connector.
That's it. you now have a 120V 30amp RV hook up as you wanted.
RVs are run on 120V 30amp, not 220V 30amp like your Home Dryer or Range.