I've never heard of a situation where the engine alternator AND the house charger don't charge the batteries. What does your dash alternator gauge say the alternator is doing? Should be around 14V. How did you determine that the batteries aren't being charged?
Or there may be a main battery fuse (or fusible link) that is blown. Or a badly corroded connection to the house batteries, or the battery-chassis ground. Any of those conditions would prevent charging from any source.
One house battery was replaced. When plugged into shore power the batteries still do not charge. but if I start the engine the house batteries charge according to the One Place readout. When I shut the engine off the One Place readout displays less then a full charge and the converter/inverter does not start to fully charge the house batteries.
It's difficult to troubleshoot electrical problems over the internet because a qualified person who is physically present will notice things going on that may not be obvious to others.
If you've replaced at least one of the batteries, chances are that the inverter/charger, the wiring, or the battery disconnect are to blame for any remaining problems. Checking voltages at each of these points with the charger operating should identify the problem. Some inverter/chargers have a variety of different modes and have to be turned on manually in addition to being connected to shore power in order to charge.
Have you checked the battery disconnect switch? If it's off then the coach batteries will not charge when plugged into shore power. You say you changed one house battery, if there is more then on they all should be the same so as not to cause a bad one from killing the good one etc:
Just had a similar problem on my '03 Brave. Batteries wouldn't take a full charge, charging systems (alternator and converter) were putting out good voltages. Replaced the batteries which seemed to work for a while but,after a couple weeks it was back to the same deal. They'd only show about 2/3 charge on my levels panel. I jacked them up a couple times using a 12amp battery charger but that wasn't fixing anything. Then one day I lost all my 12v system. To make an already long story short, I found a loose ground on the back of my 12v fuse panel. Now my batteries show a full charge all the time and my lights have never been brighter.