Just moving the White wire is not good enough. You cannot use the Double Pole, 220V breaker. You must buy a Single Pole, 120V 30amp breaker. $7.00 or so.
As for the "left side, right side". Make sure it is color to color. Meaning Black to Brass, White to Silver, and Bare to Green or Ground bar if the RV box has that. If you don't get the wires on the correct connector your polarity will be wrong and will do damage.
This is a do it yourself job, but since you are new to it and unsure, the best you can do is get that electrician out as you said. Small price to pay to ensure it is correct.