Good Weather:
Ambleside park has had a big makeover and is very good.
Lowther Castle is so much better than expected. The lost castle adventure playground is excellent.
The Gruffalo trails at Whinlatter and Grizedale can be combined with the playgrounds.
Wet weather:
As mentioned Wray Castle which can be combined with a flat bike ride along the side of Windermere or it works nicely with a green cruise on the lake and a stopover at Brockhole (adventure playground was recently closed for referb so worth checking that it has reopened) for a full day out.
Keswick pool has a slide and waves. Can be combined with King adventure.
Allan Banks in Grasmere has a nice walk through the woods, a play rooom and an art room. It also doesn’t have the NT stuffiness that many of their properties have.