If you can find what brand it is you may be able to purchase some new cartridges for it. I have replaced many cartridges in home faucets and it is very easy. You would think an RV one would be easy too.
The RV faucet may be a cheapie with no repair parts available. You could try removing the cartridge and applying some lube to the o ring gaskets/seals. Just a thought.
If all else fails, ear plugs may work!