Many MH do not charge the chassis battery from shore power or generator power.
If yours does not, purchase a $50 Trik-L-Start and mount it in your rig.
To check your batteries and a whole host of other electrical items, buy a digital voltmeter or multimeter.
Set the mutimeter to 12vdc and put the positive probe on the positive battery terminal and negative probe on the negative terminal and you will read your battery's voltage status.
A fully charged battery will be about 12.6vdc. A 50% charged battery will be about 12.1vdc.
With the coach plugged to shorepower, do the above test to see if the charging voltage is above 12.6v at the starting batteries. If so, the starting batteries do charge from shorepower and you have a battery or connection problem.
Also do check to see that the cells of your starting battery are filled to the proper level with distilled water.
The 12volt Side of Life (Part 1)