Look on the EFDSS Rootsource pages for details of the various festivals and follow the links on individual festivals. Unfortunatly for this year you've missed the opportunity of Chippenham which is one of the best as far as children are concerned. It has a very full separate events list just for children and aimed at the various age groups. Some offer fully supervised sessions others require the adult to remain in nominal charge.
Due to recent changes in the law, some festivals (especially the smaller ones) have stopped offering creche style or fully supervised opportunities where childen may be left under the supervision of those staffing the activity. It depends what you are after and you will need to check individual things. Sidmouth has a lot of Activities in Blackamore Gardens and in the Childrens Marquee up on the Main Festival site, they introduce the children to a variety of childrens games and activities with the emphasis on traditional ones such as string games, making papier mache masks, making and playing a variety of percussion instruments. There's often a circus skills workshop - the opportunity to learn to juggle or try to ride a unicycle. In the back of the Anchor is often a ceilie which includes a lot of youngsters joining in the dancing or watching from the climbing frame. Depending on their likes / dislikes try taking a gameboy, lego and puzzle books. Other things that can be useful are a personal tape player with some story books on tape, and a waterproof backed travel rug to crash out on when tired (them not you). If you are after a gradual introduction remember activities that have nothing to do with folk such as the beach, the swimming pool and the cinema. My children also inform me that Sidmouth Library has internet access (free but sessions are so popular that they must be booked in advance).