Hi,
Are your dinette lights 12VDC or 120VAC? On our rig, they're operated off the 12VDC batteries.
Does your rig have a transfer switch for shore power/generator use?
On our rig, when the generator kicks in, the transfer switch connects the output of the generator to the L1, L2, neutral lines which feeds the AC breaker panel, just like the AC shore power cord does when the generator is powered down (transfer switch is off). So it's puzzling that it only happens when you're plugged into shore power. Unless you don't have a transfer switch.
On Edit: According to your profile you have a 2012 motorhome, so it should have the transfer switch. So not sure what's going on in that case. Perhaps someone who is more familiar with the electrical systems on Monaco coaches can offer some help? :)
Good Luck finding the problem.
~Rick