Greetings Keyholeren!
I agree with Moonshot and Over59 - - if your coach doesn't need floor repairs, removing the bath fixtures open the door for many more problems - - even with very careful removal, it would be possible to damage the components being removed as well as those surrounding the fixtures being removed. My bath was professionally refinished while in-place at a cost of slightly less than $400 by a local bath refinishing firm that was recommended by my regular plumbing contractor - - the results were quite satisfactory and have whitstood two seasons plus of use with no degredation to the appearance. The before photo is below - - part of the reason for my refinish was a desire to change the color from the Avacado Green:
The after photo below shows the results of the refinish's color change to Antique Pewter:
According to my refinisher, the task of refinishing the Airstream wasn't that much different from his usual home improvement jobs - - the only difference being was that spraying requred a few more "gymnastics" that usual - - the trade-off was that the Airstream was at his workshop where he had immediate access to all of his tools and supplies.
Good luck with your project!
Kevin