Some more things to consider:
When we were full-timing, we found several RV parks that would only allow two pets. We had two cats and a dog. Even though the cats stayed in the trailer all the time, there were occasions we were not allowed entry into an RV park. Of course, being as we were on wheels, it was not an insurmountable problem, we just went on down the road.
There are also RV parks that have age limits on the RVs they will allow on the premises. Ten years of age is an oft quoted number. Any unit older is not allowed. We never encountered one of them, but apparently they exist.
We even found an RV park near Everett, WA that did not want patrons to have weapons in their "rolling home". At the time, I didn't have any with me, but I did not give them any of my money anyway. In all of our travels in MT, ID, WY, CA, WA, OR, and NV that is the only park we found that had such a rule.
As stated, one of the benefits of being on wheels is that if you don't like the rules you can get on down the road.
Oh, and when you get to your destination, please be aware that many rental homes and apartments have pet restrictions.
Good luck.
