Each individual RV owner determines whether or not you can bring your pets in their RV. When you do a search on RVshare.com for potential RVs you can rent, you can filter for pet-friendliness on the lefthand side panel. Simply go to the Additional Filter section and check the box next to "Allows Pets."
When you find a pet-friendly listing that you are interested in, you will want to message the owner by clicking on “Contact Owner” so you can discuss the details of your trip and your plans to bring a pet. Most owners will want to charge a fee or extra deposit if you are going to be bringing a pet, so make sure to let them know before you book. If you bring a pet without the owner’s authorization, they will likely charge you a much larger fee against your security deposit, so it is in your best interest to disclose all of this information up front.