Probably needs a bigger generator to overcome the big VOLTAGE DROP when the air Conditioner kicks in.
If you was monitoring the 120VAC LINE with an AC VOLTMETER you will probably see it really drop down in AC VOLTAGE when the Air Conditioner kicks on and off... Maybe the extension cord/adapter setup from the generator to the trailer is too small for the load as well...
You might get better 120VAC regulation running the TV stuff from an 400WATT PSW inverter direct connected to the trailer battery system which should run a pretty steady source of 120VAC not being effected by air conditioner kicking on and off...
just some thoughts...
Roy Ken