Thousands of RVers change their 'service address' all the time. This should not be a problem with either DirecTV or Dish, although reportedly Dish customer service does seem to deal with RVers better than DirecTV. Your problem is you got an ignorant customer service rep. The general solution is to simply hang up and call again to get a new one. I rarely have to do this when changing my service address....but actually I have had better luck using Chat on the internet to accomplish this.
Regardless of your outcome - while in Florence you should be able to get the local FOX network broadcast as I previously posted above.