Good luck! We have moved cross country twice in the past two years(NC to AZ to PA), no kids but with 3 cats, 1 dog and lots of live fish. The moving company was awesome the second time, first time we did it ourselves. It is amazing to watch them pack an entire house in a day and when they unloaded everything went right where we wanted it. Anything they took apart they put it back together and we had nothing break! I love the year we had more on the west coast, very different area and lots to explore and see before moving back east. I still stay in touch with a few friends from each place we have lived. The one was a rental and it took some time, but we did find a place that would take all of our pets.
Make sure if you haven't driven long distances with the animals before that they travel well in the car and if not talk to your vet, since there are many options. We have to drug two of our three cats, the third one could care less. They also travel in carriers with a small litterbox that is a 9x9 tin pan. I also have them on leashes with harnesses (a little worried just incase someone gets loose along the way) and they have break away collars. The harnesses and collars both have tags with our contact info. Our one neighbor before the first move thought we must have had a very sick pet, since I was taking them for drives every other day trying out meds and different dosages to see what we needed. Took three 30 min drives to find the best choice for him. The dog also either went in a crate or leashed into a seat with tags on her collar. I used shrink dink paper to make tags so they would all have enough and I could have extra incase anyone lost one while traveling.
Savannah will have lots for you to get out and explore too, so that may help. Try and relax and enjoy the time you have left where you are and go any of the places and restaurants you will miss. For the kids if they are interested get an address book so they can have their friends addresses, phone numbers, emails, etc so they can stay in touch. Maybe try and get them involved in an activity once you move or join a pool so they can meet kids their age this summer before school.
The driving itself will be hectic I'm sure, we did both moves as fast as possible because of the animals and live fish and slept in rest ares as needed. The first night in AZ we were sleeping on towels on a tile floor since we got in at 2am and weren't opening the truck up at that time.
Good luck on your move and hope all goes well!