There are a couple of ways you transfer between shore power and generator power. but the way you find the problem is the same in all cases
Method one is what you use with your Winnie.. You physically transfer the power plug from the park outlet, to your generator's outlet, this has the advantage of having a very very very low failure rate. (next to zero)
The other method is a Transfer Switch, can be manual however I may well have the only manual transfer switch in RV's
(and it only deals with one circuit) Usually it's automatic
The trouble shooting procedure, as I said, is the same in all cases.. and that is follow the wire
I like test lamps better than volt meters.. The reason is two fold.. One is a joke (A song "Looking for the Light") the other practical. With a test lamp you give it a glance, in fact you may not even need to look at it, to see "Yes, I see the light, I have power" With a volt meter you actually have to LOOK at the thing, pay attention to it. Light is just easier. I have both 12 volt and 120 volt testers.
Start at the generator output terminals.. Light good. Dark bad generator
Now follow the wire out to, ideally the Transfer switch (If you find an outlet you know what the problem is) And open the ATS box, check at the generator input to the ATS, check L1 to Neutral (30 and 50 amp) or L1 and L2 to neutral (50 amp) one at a time, if 50 amp do check both. Light good, dark bad wire or you missed a connection.
Then the ATS output. Dark = bad ATS
Then at the main breaker Dark = bad wire or missed connection
Then on the breaker buss Dark = bad or tripped main breaker
And so on