The garden is separate from the castle and you pay...

The garden is separate from the castle and you pay separately to visit the garden and there is no connection to the castle via the garden. The garden is in many ways a classic castle garden but there are some experiences for children that make it more adventurous.
The Poison Garden is a 20 minute tour of a smaller garden with only poisonous plants. The toxic garden will probably be less interesting for children.
The fountain in the garden runs every half hour if you want to see it.