If anyone was surprised by the rough treatment the OP received they must be new here. I saw it coming before I clicked on the link. What can we bash our fellow RV'ers for next? Here are some suggestions:
1) Not wearing seat belts in the living area while in motion.
2) Sleeping in the bed while in motion.
3) camping at Wallyworld
4) Buying an expensive coach but being "thrifty" / complaining about gas prices / etc
5) Driving too fast
6) Using the bathroom while in motion
7) running the furnace while in motion
8) running the furnace while fueling up
I have a 2007 Georgetown 35 bunkhouse and do not agree with your statement that they are garbage. The onan genset on your sister's is probably the exact same model that every class A gas motorhome comes with. Now, I am not sure about the 2015, but the 2007 does not have an automatic transfer switch. It has a socket in the electrical bay that you plug shore power into when not plugged in at the campground. This socket is powered by the generator. If this is the configuration that your sister has, the first obvious check is to see if the shore power is plugged into this socket.
If that doesn't help, check that there is output voltage from the generator. You can use a meter at the genset itself.
I occasionally have had trouble with the exciter field on my generator losing magnetism. My genset (a generac) actually flashes the field with every startup. I have found that if I do not get generator output voltage, I can stop and start the genset engine a couple of times and it comes back.
Good luck, and tell us what you have found.