Do I accrately understand the "programming" of the fresh water loop, the engine coolant loop, etc.?
I suspect you are a bit confused yet, judging by the way you used the terminology.
Vehicle Systems built hydronic systems they called AquaHot and also a smaller version, HydroHot, commonly used in shorter coaches. As the link you provided re. Tiffin Allegro coaches explains, Vehicle Systems changed their name to reflect their main product, AquaHot. HydroHot is not a component of a hydronic unit, but rather it is an entire hydronic unit, just a smaller capacity AquaHot. These days, since the company name change, the smaller units are called AquaHots too, and only older models retain the name HydroHot.
All models, regardless of size, have what's called MotorAide and route engine coolant through themselves to take advantage of the "free" heat, but not all models have pumps to push prewarmed coolant back to a cold engine, which is more easily started at 80-100 degrees than at 40. Hitting the engine preheat switch on a 3-switch panel, about a half hour before you plan to start the engine, depending on outdoor temps, is a good idea; and if you have an Aladdin you can monitor the engine warmup.
I prefer not to use the term "furnace" if it's avoidable. It's one unit, called a Hydronic unit (not a furnace and not a water heater as exclusive entities), that heats by electric or diesel or exchanged engine heat, both water for human use and fluid sent to remote exchangers for heating space, including critical "basement" bays. Water heating has priority and the space heating will stop during times the hot taps are turned on, in order to achieve that goal. The diesel burner heats things up vastly faster than the electric element. And keep in mind that AquaHot, Inc. is not the only manufacturer of hydronic units; many coaches have systems you will read about in this Forum called Hurricanes.
Joel