On my SOB, shore power/generator power goes to the Transfer Switch and then to the Breaker Box.
There is no component between the TS and BB................
Have you tried running the roof AC on shore power? Does the roof AC work?
If the AC unit works, then I would suspect the breaker that you shorted for the outlets. Have you replaced the breaker or tested it with a voltmeter?
The breaker marked "light" must be for a 110v light/outlets, not your 12v lights?
On my rig, three components are installed between the 110v breakers and the outlets.
First in sequence is the transfer switch built into the inverter (not the stand alone transfer switch). Second is two Breakers in the basement that control the outlets. Third is the GFI outlet near the breaker box inside the coach.
Yours may be different, but based on your description, I would try all the breakers one at a time in the breaker box to determine if the one you are using for the test is the only one that does not work.
1995 CC Magna #5280
C8.3L 300hp Cummins, 31,000lbs