I'm not a nurse yet, but for the past 3 years I worked at a hotel that had a contract with Cross Country Staffing. We rented suites (apartments) to nurses through them. Although we didn't allow pets, we allowed our long term guests (nurses, business people, etc) to have them. I have no other knowledge of what kind of agency CCS is other than we had our contract with them
Yes, but that is not practical. As an example, everyone would rent cars instead of buying them if it made financial sense. Now sometimes an RV park may have a stationary RV for rent. But as I said, RV's are not a way to save money, even under ideal circumstances (buying used in really excellent shape).
I travel with 2 dogs. One is a German Shepherd, the other is a miniature Schnauzer. I have had some difficulty, mostly because of the German Shepherd breed being on the "restricted breed" list. If you take an assignment in a vacation spot, it's not as bad. Fortunately for us, (my husband travels with me), the VA wrote a letter labeling the GS as a companion/service animal for my husband who suffers from PTSD. It has worked nicely.
I travel with a border collie. Just make sure your housing coordinator knows that you are traveling with a pet so they can place you in the appropriate housing. I'm currently set up in an apartment where the pets can go pretty much anywhere in the complex. I know of some other travelers that were placed in apartments with on site mini pet parks.