Jim,
The Magnum panel is reading the house battery voltage at the inverter. This reading will probably be 1 or 2 tenths below the actual battery bank voltage, depending on how much current you are drawing from the batteries at the time. A 10 amp charger will have a lot of trouble keeping up with your electrical usage. Your parasitic draw with just the inverter on and nothing else, will probably be about 5 amps. My rule of thumb is not to go below 12V in the house batteries. In your case, I would start restricting the electrical usage to try to keep it in the range that it is being replaced by your trickle charger when you get to 11.8 to 11.9 on the inverter panel. You may start restricting the usage a little earlier so that you do not need to turn off any of the essentials of life like the TV too early.
As for the charge rate of your little charger, If it does charge at the full 10 amps that it is rated at, 4 hours at 10 amps is only 40 amp hours. That is a long ways below the capacity of 4 golf cart batteries, and since the batteries do not charge at a 100% efficiency rate. you are a long ways from a fully charged battery bank.
The house is taking a little getting use to. Going from 10 years in a 40 foot coach to a 6 bedroom house is an adjustment. However, it is only a winter base, so we still travel 7 to 9 months a year. I got the outdoor kitchen finished a few weeks ago, so if you are in the Surprise Arizona area (NW Phoenix) sometime in the winter, stop by for a few days (I have hookups for 2 coaches), and we will grill a few steaks.
Gerald