Your assessment of the alternator being undersized is exactly correct. I even have this problem on my 2006 Alpine Coach Limited, due to the use of AGM house batteries. The AGM house batteries (eight 6 volt batteries) have much lower internal resistance than the standard wet-cell batteries, resulting in a large current draw. As a result when the AGM batteries are significantly discharged and the Vansco VMM tries to connect the chassis and house batteries with the interconnect solenoid, the alternator immediately drops from about 13.9-14.0 volts to about 11.9 volts. Since the 11.9 volts is below the threshold for the VMM, it then disconnects the solenoid, resulting in the cycling that you refer to.
Although I had this problem from day one in picking the coach up at the factory, they never did correctly diagnose the problem, even though they had me take it to 4 differently service centers for diagnosis and repair. I finally deduced what was happening just a few months ago, just by thinking about the electrical properties of what I was observing and knowing about the large current draw of the AGM batteries.
My workaround, is to run the generator after the house batteries are low, before starting the coach, so that the alternator does not have such a load on it trying to charge the heavily discharged house batteries and the chassis batteries.
However, I still have no permanent solution other than installing a 200 Amp alternator. What are the details of the isolator and sense wire removal for chassis voltage?