I've seen a lot of cyclocross bikes on the unpaved fire roads and non-technical unpaved trails (which sounds like the trail your Dad rode) I ride on my mountain bike. Sounds like your Sequoia might work fine for that with wider, knobbier "urban" tires. DH and I have also ridden our Bike Fridays (with 1.35" tires) on packed limestone park trails, and they do fine. When I do ride rooty singletrack, though, I wouldn't have anything else but my mtb with full suspension. No log jumping, teeter totters, boulders, or drops for me either, but anything really bumpy feels much better with suspension. If it's relatively smooth, you'll be fine without a mountain bike.

But then again, it's always fun to get a new bike!

Emily