Do you have 2 A/Cs on a 30 amp coach ?
If both A/Cs are running, the convertor is starving for power when the compressors cut in, dimming the lights. Low power could be the problem with the rear A/C control too. You could go through and check all the wiring on the 110 circuit breakers are tight. Then in the transfer switch anywhere there is a join in the 110 wiring. Disconnected from shore power when your doing this, of course.
Powering Dual A/Cs was the main reason RVs went to 50 amps service.
99DSDP 3884, Freightliner, XC, CAT 3126B, 300 HP /ALLISON 3060
2000 Caravan toad, Remco & Blue Ox.