I applaud the creative thinking, but I question the feasibility or affordability and it sounds like it could jeopardize your custody situation. Pretty easy for her attorney to leverage the existing stigma about living in an RV full time. If you were considering a commute anyway, find a cheaper place to rent. $2000 is not the least expensive place you could live in a manageable commute to DC.
Divorces are never easy and buying anything may lead to an issue in court. This could include an RV. Renting is usually the smart move although I get "nothing to show for it". Pick your battles.
I am no attorney - I assume you have one - these are questions you should be asking him - at least the custody jeopardy piece.
