Auxiliary generator questions

You could install an auto transfer switch to select between your two generators. You could set the priority to the onboard unit or the portable, your choice. You would need to have the 30A 120v input from the portable power both of the hot legs in your 50A service but that is easily done by someone who knows what they are doing.
The real problem is your generator will be maxed out running one standard electric heater. They pretty much all use 1,500 watts on high and about half that on low. Your generator, I'm pretty sure, isn't rated for 2,000 watts continuously, only for a surge.