The Class A motorhomes I'm familiar with all had house batteries, charging from the chassis engine, and an inverter/charger. It appears you built yours from scratch, and that's a puzzle to me. While not optimum, I think you have a start on your system. You've already made a significant investment.
It appears from your wiring diagram that the batteries are providing 12 volts (nominal) to a 24 volt inverter. This is a significant mismatch. I suggest replacing your 24 volt inverter with a 12 volt inverter.
I agree with the comment above that it isn't optimal to mix and match batteries, but I've done it and if they connected in parallel (as shown in your diagram) the system will work and all the batteries will store power for you.
I agree with the comment above that it is better to power the refrigerator with propane, when not on shore power.
It appears that you have no charging system other than solar. I suggest connecting the chassis 12 volt power to the added coach batteries so that the batteries are charged when the engine is running; this will take expertise. Also, I suggest using a battery charger to charge the batteries while connected to shore power. Better yet, get a combo inverter/charger when you replace your inverter.
Running an air conditioner off batteries and solar is a dream for many and an accomplishment for very few.