Your issue is one that I have not run into yet.
With 2 AC starting OK on shore power eliminates the current sensor(s) in the AC power panel from the picture. So it should not be a shedding issue.
The only thing that comes to mind is a resistance issue that at the time only pops up under high current loads coming on all at once.
That could mean the contacts on the generator circuit breaker have oxidized a little and limit the maximum current just enough to limit the surge current or a loose connection in the J box that connects the generator cable connections to the coach cable running to the transfer switch connections.
Question, When you start the AC units manually, have you tried to start both of them at the same time? or do you start one and then the other with a short delay.
One item that might be an issue is the ground connection between the generator ground and the chassis ground point.
The other item that might cause the issue, what is your altitude and ambient temperature status. The 8K unit should run 2 -15,000 BTU AC units and have around a 3kw reserve at 100deg. and 500ft. in altitude.