It's a hike, if your kids aren't dangerously distractible, aren't afraid of heights, and don't get too tired, they'll be fine. I don't know what previous trails they've done, but keep in mind this is not just time on the trail, it's continuous uphill effort. With a six- year-old, I'd plan on *lots* of breaks and an overall pace under 1mph - so yeah 10 hours is a decent planning estimate for Baxter peak alone.
The Cathedral trail is probably the scrambliest - I'd avoid that if you're worried about safety.
The A.T. (Hunt trail) has a couple of spots with metal handholds built in where small kids may want your help. Actually there are lots of spots where both adults and kids will want to use their hands.http://www.summitpost.org/the-hunt-trai ... eral/72445
Like gwave, I'd avoid the Abol - it's steep and it's monotonous. The Hunt has more shade, more views, more variety.
If you want to be very conservative, you can go up the Saddle Trail - that's probably the easiest and safest route, and if you opt to go over the Knife Edge, you'll come back to the same parking lot where you parked your car.http://www.summitpost.org/saddle-trail/157564
The knife edge is not difficult (one "chimney" where the kids may want a leg up), but it does have very real exposure. Certainly avoid in bad weather. If Baxter peak is your primary goal, go up the Hunt or Saddle; you can go over the Knife Edge and down Dudley or Helon Taylor if the weather is good and the kids are having fun (and you have time).