I am a spouse to an Active Duty Military member and I have a free ticket into the zoo. With my spouse I.D. am I able to buy my children's tickets at the zoo and still get the discount or is the purchase of an adult ticket required??

Yes, you should be able to

On their website it does not specifically mention the discount for children of military parents is contingent on adult purchase. So I would guess as long as you have your military ID you should be able to purchase additional youth tickets at the discounted price. (Always best to call ahead though) P.S. Thank you for your familys' service.