I'm sure I missed a solenoid somewhere in your description, I only saw one on pass. side.
Regardless, just to be sure we're on the same page, you are sure you're using the correct term "isolator"? As in a solid state block with cooling fins and 3 posts? I ask because it makes for a slightly more complicated system.
Basically it sounds like yours is like this; Alternator output feeds into center terminal of isolator, that splits it to each battery. The solenoid creates a temporary by-pass of the isolator in the case that you need to either start the generator off the chassis battery, or the m/h engine off the house battery.
I say more complicated because all you really need is a "constant duty" solenoid in the positive lead between the alternator and the house battery. The trigger terminal is then wired to a wire that is powered only when the ignition is in the run position. A simple momentary contact switch to close the solenoid at any time it's needed completes the system.
I wouldn't get too hung up on voltages yet, an isolator does just that, the different charge state or condition of two batteries will be reflected in different voltages.
