Need to pull new wire. Codes requires 2 hots, a neutral, and a ground from the main panel.
You can use 10ga for ground, but will need 6ga minimum for the hots and neutral and a 60A breaker.
The reason being, if you kept the 10ga wire, there is a possibility for an overload if using more than one of the receptacles. Not to mention that those boxes are wired for 2 buses with 2 120 lines.
I did this same upgrade a couple years ago and have not regretted it. Having a port available for my welder has been nice too.
If you don't want to do all this, can you use an exterior receptacle on your RV as your "convenience" receptacle?