We travel with our 2 cats. They never go outside. Never have had issues with dogs although there are some inconsiderate dog owners out there. The critters settle in pretty fast when we finally get set up in a spot. Only issues we have are when traveling. One travels well and one not so well even though he is getting better with it.
Even though cats are fairly self reliant they are still social animals and don't like being left alone for long periods. You are their "family" so I hope you will take them along with you no matter how long or short a stay you plan on. As stated before, start getting them used to riding in your truck now. See how they react on a short trip around town.