I personally would skip the bunkhouse and look for something that has reasonable sleeping accommodations for your family, which shouldn't be too hard. Yes, it would involve converting a dinette and/or sofa to a bed each night (and back in the morning), but compared to a pop-up that's fairly straightforward. Bunks take up a good bit of space and weight and tend to be rather cramped and short often. A cabover that can sleep a couple of children is not hard to find. The cabover bed on my motorhome is actually a bit larger than the bed in the back.
Particularly with children, it often works well to bring a (cheap) tent along and if the weather and campground are amenable have some of them sleep in it (and presumably be responsible for setting up and taking down the tent). This doesn't need to be a top of the line tent by any means; a $50 or less dome tent should work okay for this sort of use, though it may not last as well as a better tent.
There is next to no difference in gasoline usage between a 28ft and 31ft class C. You could reasonably expect somewhere around 8 mpg, give or take 1 mpg or so, for most class C's (built on the Ford E series or equivalent Chevy chassis--the Chevy ones I gather tend to do slightly better on average).
Most gas class C's will probably have the Onan 4KY generator (which has had a few different model names over the years--basically it's the 4 kW Onan generator). This is a reliable generator if its taken care of and gets use reasonably regularly. It generally won't come on automatically in the event of a power failure, at least without some additional auto-start gizmo. A motorhome does not heat up in the summer sun or cool down in the winter anywhere near as quickly as a Suburban or passenger car; there's some actual insulation in the walls and ceilings.
My motorhome storage consists of parking it next to my garage. I charge myself a very reasonable rate.