I wouldn't worry so much about how he will be on your trip. You have everything you need just starting with the rv.
We were living in an rv for about a year the first year we had both our chis in Fl. One is only 2 lbs and the other is 7 lbs. We did use a playpen; especially for the smaller one. They were just always where we were and loved to be on the bed staring out the window more then anything. What we didn't prepare for at first, we added but honestly they just were always kept on a leash, in the rv or the playpen.
We left during Hurricane Irma and could only take a few things from our choices. We even had a cat in the mix. We had to choose between the playpen and the kennel stroller and ended up choosing the playpen. We were kind of floating (like a lot of people from Fla) after the hurricane but rode away from it until we hit North Carolina. We had stacked our truck with gas tanks and luckily found literally one gas station at a point we couldn't go much farther in Georgia so we ended up staying in the truck for almost 16 hours straight for all the bad weather, etc. When we got to North Carolina, we bought a tent and basic supplies, a harness and long leash for the cat and extra blankets. It was Sept so still some really cold nights. We had a lot of clothes and other things for them for night and we had a lot of blankets. The rangers were giving all of us from Fla after the hurricane free firewood so we had a great time but did end up sleeping with the chis and cat in the truck at night while our teenagers mostly stayed in the tent (larger suv). We used the playpen A LOT! We did always have them on the leash with us and were most worried for Bella staying warm. Well we did have a little emergency for Bella with her teeth and had to find a local vet but everything turned out fine and we just added as we went along.
We stayed at a hotel for about two more months after that in our move to my home in NY (once everything was settled from the house damages) until our home closed here in NY around Christmas. These were unplanned adventures and we did what we could but had a good time in the mix and the chis were really always happy and adjustable. We had been told about animals by the rangers as a precaution to make sure the animals were in either the tent or car with us. Now other dogs and pets were another story....
. And finding a hotel that would let us stay even with little chihuahuas was a nightmare but afterward, they really did adjust. I can't say enough how much the play pen really helped us so much (one of those pack and plays). Even in the hotel.
You should have a great trip with your chi! It's a lot of fun.