I've taken my stall to lots of one-day festivals, like Strawberry Fayre in Cambridge. One-day events are often free, so if the worst happens, you havn't lost money. Also with no camping involved, taking children is not so daunting IMO.
Lots of weekend festivals allow you to buy a day pass. The Womad festival at Reading is meant to be particularly child friendly, (it might even have a creche, and definitely has baby changing tents etc) and you can get a day pass.Is it on this year? usually held at the end of July I think.
Also the Larmer Tree festival is meant to be family orientated, I think.
I've happily taken my sons as babies to one-day festivals, and also felt OK about taking my older son once he hit 5 or so. Toddlers are another matter. When they are too old to sit in a pushchair and take naps, yet too young to be let loose without constant watching, festivals can be too stressful IME. Mud, mud, mud, a random scattering of stall holder's electrical generators and cables, wobbly stall frameworks swaying in the wind, rails of clothing just waiting to be pulled over, loud music infinitely boring to small ears, fragile but expensive craft items within toddler reach, dodgy-looking dogs, unstubbed out cigarettes lurking in the grass, ohhh I can feel my stress levels rising just thinking about it..
Have fun!