We are not full timers, but we do travel with one cat. Have seen people traveling with multiple cats. It is much easier to travel without them ;-).
Each cat is different. Ours will walk on a lease and we try to get her out in some fresh air once a day. She has escaped twice but we were able to get her back each time. It was stressful.
It is a learning experience. We make sure we know where she is in the motorhome before opening the door. We made a folding barrier for the coach door so we can more easily get inside then remove the barrier. As she gets more accustom to the motorhome and we get more accustom to "where is the cat" before opening the door things are working out pretty good.
I guess part of the equation will be "how big is the living space for 3 cats and adults? Also, three cats may not be as likely to bolt out the door as they have each other for company.
