Hey Captain, Your Example #1 needs to be split into 2 parts:
- When the vehicle engine is running, a solenoid switch ties the chassis battery and the house battery together, so that both batteries are charged by the alternater. It's a dumb brute-force system, but it works.
- When the generator is running, 120 volts is applied to the house wiring, just as it is when you connect to shore power. The very same 120 volt>12 volt converter which charges the house battery when plugged into shore power charges the house battery when the generator is running.
- If you are running on shore power, the house battery is being charged by the converter OR by the solar system, depending on which system happens to be providing more voltage to the house battery at any specific time. The systems do not interact with each other, they simply look at the house battery voltage and provide power, or not. Simple. If there's no sunshine, the solar system won't be working. No manual intervention is needed
Now, on the other hand...
There are high-zoot systems you can buy to integrate all this and allow you to automate what's going on.... automatic generator starters...automatic load shedding...shore power augmentation from a solar system....etc...etc.
But why go to all the trouble.
BTW my name isn't Bob.