Come out of CDA and head for Alhama. Then take the A7 signposted to Murcia. When you reach Murcia follow signs for Alicante, the road changes its name temporarily to A30.
On the A7 all the junction numbers are in the 600's when it changes to the A30 they are in the 100's. Turn off at junction 136. It should be signposted from there, its only 5 mins from the motorway, you may be able to see it up on the hill on your right before you turn off.
Its a good day out as long as the kids are big enough to go on the slides. I have never been to the zoo next door but I think you entrance ticket allows access to both facilities.
Take food and water, (and sun cream and towels),