I can think of a few different ways to make a split system with about half on the house and half in the RV. They don't need to match, and they can even use different equipment.
The first thing that comes to my mind is to do a DC coupled setup. On the house, use something like a Skybox or Sol-Ark, or even the Schneider XW-Pro like I have, but then you also need the solar charge controller. The other 2 have one built in. Have your important loads on the backup panel after the inverter, or make sure the inverter can sell back to the grid input side. Have this system run in a battery priority or self consumption mode. All 3 I mentioned can do that with DC coupled solar. My Schneider has issues with AC coupling and grid sell.
The RV system should be a DC coupled setup. That way it can charge anytime there is sun, even with the inverter shut down etc. When not docked, the systems are completely separate. When little load is used in the RV, it will top up the batteries, and curtail the solar. What a waste of power when the RV is parked. When I first started to think about this, I thought the most efficient would be to tie the battery banks together. But that does pose one big problem. You need to get the systems to the exact same state of charge / voltage to do that. If the RV is all topped up, and the the house is down at 40% charge, the current surge would be crazy. AC coupling might work, but I think that would be another whole issue. The RV system would have to slave off and "Grid Sell" back to the home. I know I could make my Schneider do that, but do you need a 6,800 watt inverter in the RV? If that seems reasonable, you can run an AC cable, turn on grid sell and tell it how many amps to push. It will happily pump up to it's full 6,800 watts from the RV battery into the home breaker panel. I have mine only doing 1,700 watts for 5 hours each evening to save on time of use billing. This way, I still have 50% of my battery left if there is a power failure overnight. So this AC couple setup may be an option.
But if the home is also going to be a hybrid setup with a battery bank, I think I have a more elegant solution. Let's say the RV is a 3,200 watt system, but with the panels flat and some trees around, it is able to make an average of 2,000 for 4 hours. That's certainly usable power, and it may do better. But as a worst case, let's call it 8 kwh a day that we can take from the RV. Just use an AC mains powered battery charger that is powered from the RV system, and charges the battery bank in the home. That is just a 300 watt charger running all day off of the RV. I have a 600 watt one here that I use for charging my e-bike batteries. You can connect it to a timer to control when and for how long it will push power out. Have it run when the sun is down to help keep your home batteries up overnight. Or during a higher rate time of use etc. With this setup, you don't need any special equipment on either end. The inverter in the RV just charges the home battery. Everything else is a normal DC coupled system. That 600 watt charger will push 8 KWH to the house in just over 13 hours. If the solar does better, you can run it longer. Obviously have a low voltage cut also, so the charger to the house will just shut off if it pulls the RV battery bank too low. Using this setup the RV does not even need to be the same voltage or chemistry etc. I have actually thought about getting 2 or 3 of those 600 watt chargers to run off of my old gas generator to top up my battery during a power failure. I can connect the generator to the AC2 input on the Schneider XW-Pro inverter, and it will be able to charge at up to 5,000 watts, but I would have to disconnect my AC coupled solar to do that. If I have the generator run the DC chargers, it can all run in parallel.