M.P.
How about Spring Valley?! It has a farm at the park where the kids can pet some animals and even help feed some of them. My son who was about 18 months the first time he went there enjoyed it. Even helped feed one of the cows.
Did you just go to the Schaumburg Park District website? It lists the types of recreation at each of the parks. Here's a link to Spring Valley on their site.
http://www.parkfun.com/recreation/SpringValley.aspx