I've bouldered on that upper tier, though it was a bit pants. The path round to the east of the crag is usually pretty clear, but I can see you'd struggle if it's not had much use, you've got 2 little ones and a pad; it's pretty steep, but there is usually a nice flat area in the middle of the crag. Bowden is on the list but would probably do it midweek.
Berryhill would probably be good for kids too, slightly longer walk but an nice spot once there.