OK - sounds like a deafening "No!" to camping?
What do you fancy then? Brockhole is very child-friendly, and the cafe serves delicious food, and it's fairly centrally located. There's an adventure playground there, and some indoor exhibitions and stuff if it's wet.
It's free, but cars cost £4.50 for whole day (£3.50 for 4 hours).
Alternatively we could meet somewhere like Tarn Hows - lovely walk around the tarn, (good surface for buggies and wheelchairs). Not much in the way of facilities though.
Or we could meet at Haverthwaite and go on the train and/or boat? Stopping for a picnice somewhere?
What does everyone fancy?