AC trips out on shore power but not when on the generator

You can check voltage at any regular house-style outlet in the coach.

With 30 amp, there is a single hot, so A/C and outlet voltage will be the same.

Also, with shore power disconnected, generator off and inverter off if you have one, open the ATS and check that all connections are clean and tight. Could have a problem there, at the male or female end of the shore power cord or the connections between side of coach and ATS (if the shore power cord doesn't connect directly to the ATS).