The regulator should be powered of the start battery. Because if the house is dead. You'll start the engine. But the alt will never start charging.
The relays sound dumb. Simple is better.
But the b+ goes to the engine battery switch. (Starter post is easiest) it draws ~7a and can not be on the ign line. And the on/off goes to the ign
Keep alt power and sense to house battery.
The parellel is fine. Unless the vsr also does
shore power charge sharing. Which the soliniod will not.