As I see it, you've got 4 choices, short of putting the dog in a kennel while traveling. (Boo!!)
1.) Wash the dog. Trim their nails.
2.) Tuck an old blanket onto the seat before leaving.
3.) Place a box or basket in the seat to deny the dog the seat, but it probably gives them a view out the windshield so they can watch for your return. They'll learn to climb on the back of the sofa, passenger seat, dinette, or table to see out of the RV.
4.) Buy some tailored and fitted cover that you'll have to learn to sit on, getting dog hair on your clothes and not enjoying the original (leather?) seat cover.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI