A multimeter used during your troubleshooting will greatly aid your efforts..
.. you know the gensets are good
.. your Alpine works fine from shore power plugged into 50 amp outlet
Your shore cable is most likely HARD WIRED ON the Alpine side.. unlike mine that uses a plug in receptacle.
You can’t just swap in another’s shore power cord easily
I would be looking at the adapters you are using to connect genset output to your factory shore power male plug end.
It is also a very easy and quick test to verify your hardwired shore cable male plug end into the power center panel AC BUS bars
If you you have some basic skill sets and a multimeter then disconnect shore power cable
Drag the male end plug into the RV to your power center panel
Remove panel cover
Set meter to ohms X1 scale
Now measure from each Main breaker feed line coming into the two main 50 amp breakers to the plug ends
Looking for less than 1 ohm reading on Red wire and black wire (L1 and L2) 50 amp feed lines
Repeat same process for large white wire on the BUS bar (neutral) and then ground wire
If all four connections from power center to each respective plug end read less than 1 oh, the shore power cord l male end and hard wired ends are good
This also is checking the slip rings on that fancy cord rewind wheel
My poorly made video shows you how to perform this trst to verify your shore power cord from the male end plug clear to the main BUS bars and circuit breakers on your power center panel
https://youtu.be/9XtRxHNejXs
use caution when working around energized circuits .. in this case you have the male 50 amp plug pulled inside the RV to do the above test so you know the 120 side of the power center is safe..
The 12 vdc side of the power center is still powered up so turn off the battery cutoff switch if needed