Craig is absolutely correct! A three prong has only ground, not neutral. The smaller, probably bare “equipment ground” is not supposed to be a current carrying conductor. If you insist on using it as is, will it work? It will seem to be working, but in reality, as Craig said, you will be putting anyone that comes in contact with that RV at risk of shock and yes possibly electrocution, (that means death). Also, since it was mentioned that the ground is smaller, and bare, if enough amps are flowing, that bare conductor in your RV will be getting very hot. So hot, that it can cause a fire before it shorts out to the hot because it melted the insulation. If you are still not convinced, let us know.
Always practice safety! The life you save may just be your own!