Any recommendations for pleasant and easy climbing with 9 &11 y.o. in White Peak, staying in Hartington? Yes there is Windgather, but as it won't be for long it would be preferable to stay local.
You could pop over to Harborough Rocks, near Brassington. It’s close by with great landings and massive pockets. My dad used to take me there when I was a kid. Great fun. Harborough Rocks
I would second the Harborogh suggestion. Juggy pocketed limestone with quite short routes. Should be possible to set up top ropes on trad gear. Routes on RHS especially amenable.
Aldery Cliff would be a lot closer but doesn't have much that is really easy. I've taken small kids up Clothesline (S 4a) and a bottom rope can be arranged but you do have to lead it first or ab down, which is a bit a faff.