I am assuming this is 50 amp service. This connection feeds 120 volts in to your rig through 2 different lines. If you lose one line the other will still power half your rig. It is normal to have one AC on each leg.
Since it works on shore power you have narrowed it down quite a bit. Like Grumpy mentioned, I would start with the transfer switch. Tighten all connections with no power applied. You can measure the voltage coming from the generator at the transfer switch. If you measure it coming in but not going out, the switch may have a bad contact.
If you don't measure it coming in, the next check would be at the generator. Loose connection, bad or partially tripped breaker, or perish the thought a failed generator.
Voltage tests will tell you where the problem is.
__________________
Jim
Retired electronic technician (45 years in the field)
2017 Greyhawk 29W (solar & many other mods)
wife (maybe I should have given her top billing)
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