Jeremy,
When the engine is running, the house batteries are receiving the same charging voltage from the alternator that the chassis batteries are on your coach.
The two battery banks on your coach are separated by a large diode called a battery isolator. The battery isolator lets the alternator charge both battery banks evenly, but the current can only flow in one direction, from the alternator to the batteries. Since the current can only flow in one direction, one battery bank can not discharge into the other bank. Therefore the batteries are isolated from each other while still being charged from the same source.
You said that your engine alternator was charging at 14.4 volts. Is that cold, when first started, or is that when the alternator is hot after running a while? Although that is within the range for an alternator. It is on the high end, especially if the engine has been running a while and the alternator is hot. I like to see 14.1V to 14.2V when cold with good batteries and 13.8V to 14V when hot. Your cold charging voltage will be less if your house batteries are discharged, and they have to be recharged before the alternator can produce maximum voltage.
You said that your coach batteries were only two years old. A set of good quality coach batteries that are properly maintained should last 6 to 8 years. As your coach has 6 coach batteries, you may want to check the batteries before you discard $600 to $1,000 worth of batteries.
Gerald