Both Birches Valley and Marquis Drive have playgrounds and big green spaces close to the cafes for kicking balls around/throwing frisbees too.
Birches Valley has nicer walks suitable for kids, including the fairy grove (they’ve carved little houses into the trunks of the trees, with little doors on hinges. It’s ace. And it has a bike shop, which I’m sure the kids will love. 😛 Also has the best ice-cream.
Marquis Drive has the War Hut that has objects from World War I (including weaponry) – Cannock Chase was an army training ground (it’s where Tolkien trained). It has a gift shop which used to have terrifying stuffed animals in it, not sure if they’re still there…
Think parking is around £1.50 for an hour or £3.50 for a full day at both, not sure of the exact number though.