Claife Heights/Wray Castle/west shore of Windermere. Various routes can be linked together but there are some unavoidable climbs.
Coniston village north to Tilberthwaite. There is a lovely bridleway that runs along the main road…it’s not shown on older OS maps. Again, bit of a climb after that but lots of riding around the old quarries and Hodge Close.
Loughrigg Terrace loop from Ambleside.
Grizedale exploring, bridleways and bits of the forest tracks and purpose built stuff.
My kids have done those routes over the last few years, Hazel had probably just turned 7 when we first did them.
It’s up to you to know what your kids can do, spend lots of time with 1:25 maps and study the contours. My kids seem to prefer short but steep ups where we can push and chat if necessary. Longer grindy climbs are more frustrating for all of us as they take ages and get knackered quickly.