Greenbelt is brilliant for kids - my dd is now 13, we've been going since she was 3. The last couple of years I have only seen her when she has run out of money ;)
As folk have said, the children's area will have big queues however getting them in there will give you a couple of hours to explore alone and the activities are good. There is also loads going on onsite for families and the site is very family friendly and safe. You can download a copy of the daily diary from the website for a few quid which might help you plan your days in advance - or just get a paper copy once you get on site and have a planning session.
It is worth getting to site early on Friday if you don't want to end up with your tent miles away! There will be a queue of cars to get on.
There is loads of nice healthy food to buy - Nuts Cafe is usually good if a bit busy. We volunteer onsite and never do any cooking (no time) so if you can afford it then there is nice food, it's not all burgers and chips! Worth bringing water and cereal bars etc. though as you can spend a lot just on drinks. I don't think the food is particularly pricey compared to similar events. There is usually a convenience type store with milk and other basics as well.
Bring clothes for all seasons, I am convinced Cheltenham has it's own climate, I've been frozen and burned on the same day before. A lot of the festival is on racecourse facilities so it isn't a big muddy field - and some things are indoors not in tents so it doesn't tend to get too bad even if wet.
You can charge mobiles for a small fee in "The Tank".
Arrange a meeting point with your kids for if you get separated, somewhere they can see easily all around. A good place is next to 'the arena' as there is usually an information booth there, where someone would help them and you if you were separated.
Hope you enjoy it!