I just finished residency and moved 1300 miles by myself with my dog (13h day 1, 8h day 2). It is easier with more than one person since someone can sit out in the vehicle with the pets, but other people might be moving alone so I'll add my two cents.
For the dog, I found that stopping at the state "welcome centers" when you first cross into a new state was best for letting the dog stretch his legs and pee. They're off the road enough but not so awkward to get to you get turned around, and they had restrooms for humans too. I think the big welcome centers are kept cleaner than the smaller rest areas in other places along the way. Only one said no pets on the building entrance door, but I took my dog in with me anyway and no one said anything. I tried to load up on snacks and drinks early in the day when it was cooler and the dog could wait in the car for <5 minutes and be okay. I would hit a drive-through for meals but sit and eat in the parking lot because it didn't seem that safe to be driving a loaded-down car where you can't see out of the rearview window that well, with a dog in the front seat, on the interstate, in a place you've never been all while eating, haha.
If you haven't ever driven that far before, I do think splitting it up is smart. Especially if your SO hasn't driven a truck/trailer that large before. La Quinta hotels are all pet friendly with no extra pet/cleaning fees, if there is one along your way. Some are nicer than others...the one I stayed at in Little Rock was not that nice but it was <$100. I've also stayed at a Best Western and a Hampton Inn that were pet friendly before, which were nicer, but they charged an extra $50-75 for the dog. If you're stopping, you don't even necessarily have to stop halfway...even if you were to drive 9ish hours (10-10.5 with stops probably), your second day would be a shorter 3-4 hours so you may be more energized when you arrive and have to unload the moving truck. When I moved out to my residency location it felt weird to stop just 2 hours from our destination, but it ended up working out really well and we had the entire truck unloaded by very early afternoon.
I recently started using Waze for navigation, and the hazard and police alerts were really nice during this long drive. Audiobooks help pass the time, and I also made a playlist of my favorite songs to sing along to. Called my mom and talked for almost an hour too.
It may be too late to get them now, but I highly recommend pet seatbelts for anytime an animal rides in the car. At least buckling in the cat/sugar glider carrier is a good idea. Winston has a seatbelt from Ruffwear. It has a large chest plate to distribute the pressure it he were to be thrown forward, the buckles are metal, and it attaches to the human seatbelt. He can lay flat, curl up, whatever, and I get to feel more secure that he won't go flying through the window in an accident.