What you need is a touring bicycle. Thats because touring bikes have low centers of gravity, making them more stable. Their frames are a little beefier than a road bike. And they have gearing thats like a mountain bike, so you can easily pull a big load up hill. The rear axle isnt really an issuea trailer of 70 pounds (trailer plus child plus accessories) probably has a tongue weight of only 30 or 35 pounds, and not much more than that when pulled up hill.
One classic example of this type of bike is the Cannondale T800 ($1,400; cannondale.com), which I sort of regard as mid-range, at least compared to some of the all-carbon road-rockets out there. It has an aluminum frame; a stable, relaxed geometry; lots of gears; sturdy 36-spoke Mavid rims; and tires that are plenty fat enough for even fairly rough trails (700X35 Continental Top Touring tires). This bike is designed to carry/pull a load, so the trailer should pose no problem.
Treks 520 ($1,240; trekbikes.com) is similar in all the important ways, save one: It has a steel frame. This makes for a slightly heavier bike, but one thats probably going to ride more smoothly. And weight isnt really an issue hereyoure already packing plenty, so another pound or so isnt going to matter. Its worth a look.