The RV is your domicile while you are living in it just as a hotel or motel room would be. There should be no problem with having a firearm in the coach; but I would not declare it if stopped just as I would not declare a firearm in my principle place of residence.
Check the domicile laws in the states you intend to visit.
Gun Control: The premise that a woman found in an alley, raped and strangled with her own pantyhose, is morally superior to allowing that same woman to defend her life with a firearm.
"Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house." - Jules Henri Poincare
"Three thousand people died on Sept. 11 because eight pilots were killed"
-- former Northwest Airlines pilot Stephen Luckey