Agree with our(OP's) diagnosis. If everything works on generator, but not real 50 amp shore power, you have a problem in the shore power cord or ATS.
But, start by verifying that you do have real 50 amp service at the outlet.
IF YOU ARE SAFE WORKING AROUND 120/240 VAC POWER:
Outer straights= hots.
Center straight= neutral.
Center round= ground.
So, either outer straight to either center straight or round= 120 VAC
Center round to center straight= 0
Outer straight to outer straight= 240 VAC
Next, check male end of shore power cord for overheating. If shore power cord is not hard wired, use ohm meter to check that continuity through the shore power cord.
If the outlet and shore power cord checks out (or shore power cord hard wired on coach end), turn off inverter, generator off, shore power disconnected: Open ATS (Automatic Transfer Switch) and check there.