So, I wonder what the choices are. If you leave the cat with a friend or relative, or decide to rehome the cat so you can travel and I know it sounds like someone wouldn't possibly consider that but it happens all the time with both dogs and cats, there is the same possibilities as if you take the cat along. The cat may get away from the caretaker. I know someone who gave a cat away and the cat returned looking for the man. The cat returned in the pouring rain wet and hungry. He came to our RV door (we were full-timing at that time) meowing when he found his previous owner wasn't home. The previous owner took the cat back in.
I cannot stress too much how much your stress levels have an impact on your pets, both dogs, cats and even our guinea pig. A pet is happiest with their owners despite crating or leashes. I would buy a halter for the cat and keep it tethered with a lease even in the trailer until the cat grew used to the routine. I have bought leashes for the dogs that hook to the seat belt and when released, I am already to walk them. Anyone looking for different supplies, I suggest JeffersPet online as I have shopped with them for probably 20 years and they have a good selection at reasonable prices.
I have traveled, camped and relocated with dogs, cats, guinea pigs and gold fish over the years and met many, many people especially when full-timing that traveled with pets of all sorts. Only once did we leave our pets in a kennel and I worried about them every minute. The cat was extremely bitter about the experience. We checked out a kennel before going to Disney World once and although nice, we hauled the pets to Disney with us and kenneled them there checking on them and walking them 3 times a day.
Attitude? We are going to do this and it will be fine goes a long way in getting something done. If we concentrate on the "what ifs", we end up frozen in time. I could give you a list of "what ifs" that might make you never want to even leave your house again.