I agree to pass on the RV. Our last PCS, we towed our camper but stayed in hotels the entire way from the Midwest to Southern California. Unless you're planning on staying in one location more than two nights, it's a total pain to have to constantly hook up hoses and drain tanks, etc., every night and every morning. After a long day on the road, you want to get to a room and relax, not worry about setting up camp.
There are many hotel chains that are dog friendly and, with an 8 lb dog, you won't run into too many issues with size limitations. Last PCS, we moved our goldfish in an ice cream pail. Next summer, we'll being moving a large dog, the same goldfish (it's moved multiple times with us, seriously), a hamster, and a praying mantis. Not looking forward to figuring that one all out. Anyway, we always try to stay at hotels that offer breakfast as part of the stay, we have a cooler for sandwiches for a stop at lunch (refill the cooler with hotel ice each morning), and then dinner on the road. With a young one, we would try to do the lunch stop in a city that had a playground close to the highway so that our kids could run for a little bit. Oh, and Red box is awesome for getting movies on the road.
When we did the move I mentioned above, we shipped a vehicle from Chicago to Palm Springs; it cost approx $700. That was in 2010 and, as we all know, gas/diesel prices are higher now. I would assume costs to ship a vehicle will be even higher now, especially going all the way cross country, I don't believe that shipping a vehicle is covered as part of your move. We had to pay for it ourselves, however, you should be paid mileage on both of your vehicles so that offsets the cost. We have always done a partial do-it-yourself move which has made is beneficial to us to try to move some of our belongings in the vehicles. Getting quotes for shipping a vehicle is easy since there are many online services that will provide you with quotes from multiple drivers. Any chance you could rent a tow dolly from UHaul, one way, and tow the one car behind the larger car?
We are four years from retirement and are looking forward to a PCS next summer, mostly for the fact that we will again purchase a home. We have always sold any homes we have purchased when we had a PCS, the last in 2008. We have rented the last almost five years. In that five years, we have paid $105k in rent. That pains me to say because we have paid someone else's mortgage while getting no equity to benefit us after retirement. Only you can make the decision on whether or not to sell or rent your house here in California. If you 1) are in an area that has lots of military coming and going, 2) the rent you would be able to ask would cover your mortgage, and 3)you can cover mortgage if the house is empty a month or you have maintenance expenses, I would seriously explore trying to keep it as a rental property. I wish that I had the "balls" to have kept our last house as a rental so that even though I was paying that $105k somewhere else, at least I would have been getting equity in a hard asset via a renter. On the other side of the spectrum, one current landlord has four homes right now (one they live in and three rental properties). I don't recommend being that real estate poor but I also don't think it's a bad idea to consider trying to keep one house. Just make sure you're able to deal with maintenance costs when they're needed to be dealt with (we waited two weeks for a new refrigerator in August while our landlord tried to get the best "deal" on getting it repaired/replaced.)
As far as prepping for the move, two PCS's ago, we had to attend a TMO presentation on filling out the paperwork, how to handle dealing with the movers, info on the partial do-it-yourself move (I think it might be called something else now but I know it as a DITY move), etc. See if they have that available since it will tell you everything you need to do and what reimbursement you may have coming to you. If I remember correctly, you should have a certain amount of per dium for each day of travel to cover food and lodging. I highly recommend taking pictures of all your furniture so you've got proof of condition, especially if you aren't doing a door to door move since you're household goods will be touched more if it gets put into storage in NC awaiting your arrival. Talk with the driver about when he'll be leaving and estimates getting there. Sometimes they pick up other things en route and put it in the truck with your stuff. It's nice to know that. I also recommend asking the driver to call you with your weight after it's taken. I've found that whenever I don't ask, our weight is suspiciously close to our maximum weight allowance. I'm sure that this affects how much they get paid and can limit how much reimbursement you get if you decide to move some of your belongings during a DITY move. If you know early enough, you can request a re-weight just to make sure that it's the correct weight.
Hopefully this hasn't overloaded you more, I really could go on. We have been there, done that, and are proof that you will survive. Just remember to breath, don't be afraid to call TMO with questions, be prepared to be flexible, and, if you can, take in some sights on the drive cross country.