There is a decent cinema in east Grinsted, a cool Everyman one in Oxted and a massive one in Crawley.
Baby groups and whatnot in east Grinsted, Lingfield, Oxted and Edenbridge
Not sure about soft play but I'm sure there is.
Ashdown forest is full of excellent children's tails/adventure playgrounds.
Dormansland recreational ground or "the park" is alway busy with mums and young kids and they are very friendly. Expect to meet people and chat there if that's what you want.
Because there is so much glorious countryside around DD spent her formative years (still does) playing in the woods, making dens etc.
If you do move there - let me know and I'll
Send you details of some of the excellent t walks up over the farmland/start of the high Weald.
The ones in the woods/golf course are obvious but I lived here for years before I workers out/realised that you can walk all over the beauty hills you can see on the horizon - and there are paths direct from the village (high street)
I would 100% recommend living here. It's quiet, friendly and beautiful - and though it is a little village it's very close to lots of big towns with loads to do.