As long as your fish are not aggressive towards each other, I would keep them together. A cooler is a great idea, but if you do not have that you can buy totes. Walmart sells 45 gallon totes, which would be more than adequate to fit all the fish in the 55gal into (though, sloshing might become a problem during the drive). Because you have a 16 hour drive ahead of you and possibly wait time at the destination before you can set up the fish, you will need to handle filtration, oxygenation and possibly heating during the drive. If your car has a power outlet, you may be able to even use your existing filter plugged in (depending on what kind of filter it is - this is probably workable only for small canisters and sponge filters). If your existing filter will not work for the drive, you will need to place sponge filters in both of your tanks right now to start growing BB on them, and use them during the drive. If you have live plants, having them in the same tote(s) as the fish will be beneficial. Depending on where you are driving from/to, you may also need to heat the water. Same as above, if you have a plug in your car, use a heater in the tote/cooler, but if not, you will need to use external heat packs or a battery bank to power the heater.
I have a recurring dream about doing this one day, in my dream we buy a house on the coast and have to move the fish
The way it works in my dream is that at 3-4am, everyone shows up at the house and starts to break down the tanks, I have an army of friends each who have been assigned a task (taking out the gravel, emptying the water, moving the fish, adding clean water to the totes, setting up sponge filters and heaters and hooking them up to power in the vehicle, etc etc), and we work methodically and in ~3h we have the tanks empty, loaded into a rented uhaul van, and the drive begins. At rest stops, we check on the fish and make sure the equipment is functioning and water is in good shape temp wise (in some versions of the dream I test for ammonia and nitrites at a gas station and add prime and amquel to the water...). At the destination, we have a bare bottom holding tank set up that has been calibrated to roughly the same water parameters as the fish are coming from, and the fish and water from the totes go into the holding tank along with the plants tossed in. The existing filters from the tanks are hooked up to the holding tank, and everyone goes to bed. crisis averted until the next day.
Feel free to tell me that I have weird-ass dreams