Definitely Monsal first as more to see, though they all have interesting quirks depending on your kids.
As above, High Peak Trail needs to start at Middleton Top to avoid the two killer climbs which will put kids off. Not much to stop at along there either.
Tissington Trail has a bit more to offer, lovely village is Tissington, tea stop on the trail, Cafe in the village. Signal box at Hartington to look at. A couple of miles up the trail from Parsley Hey is the Royal Oak at Hurdlow which does great food, if a little pricey for a family.
Depending on age, the trail round Carsington is OK, but the far side has some short sharp ups and downs for little legs, so not what you really wanted I guess.