Road/Mountain/Hybrid/Touring, you need to look at gear ratios basically. w/ hills I lug my kids around (~65# total, add 20# for trailer, more for whatever other luggage is in the trailer), I need a gear ratio <1 available (rear cog w/ more teeth than smallest front cog). People in better shape in flatter places w/ smaller kids could maybe do fine w/ off-the-shelf roadbike gearing.
I can take one kid, but not both, up the hill to home in the lowest gear on my road-like bike, 30/28.
I just about never drop to the bottom gear on my mtn bike pulling the trailer (22/34), but I do get to the point where I'm going <7 mph, and when I'm doing that I want to make sure I have either good shoulder or sidewalk 'cause that's below my straight-face cutoff of where I can be in the traffic lane and not feel guilty.
Anyway, regardless of the frame, chainrings and cassettes can be juggled to get whatever gear ratio you need, derailers permitting, to pull your kids up your topography. Keeping in mind that the kids keep growing, maybe even faster than you wear out cassettes and chains.