I would definitely check the fluid levels in your battery. This is usually what happens when your battery has perhaps boiled out the battery fluids and maybe you now have a bad cell in the battery. A fully charged battery should read 12.6-7VDC at the battery terminals and when you hookup to shore power this same DC Voltage level should jump up to 13.6VDC telling you that your battery is being charged.
When on shore power the on-board converter/charger is attempting to charge your bad battery which may be the cause for the diming of the lights etc...
If the battery checks good then this could also be the first symptoms of a failing converter/charger unit....
You need to monitor your 12VDC voltages both when just using the batterey and also when you are plugged into shore power...
The 12VDC is changing levels on you causing the diming of things...
Just my thoughts and guesses...
Roy Ken