Can I take my ex-wife to small claims court over a dispute on daycare expenses?

No. No small claims court.
OK, disclaimer because I am not licensed in IL and I'm only answering your question due to the fact that you asked it 7 days ago and no one has answered.
Different courts have different jurisdictions. For example, a copyright infringement belongs in Federal Court. A car accident case, 99 times out of 100 belongs in one of the state courts, like Superior Court, District Court, Municipal Court or the like. Family law stays in the Family Court. I sense that you may not have been thrilled with the court in which your divorce was finalized, but that is the court that you are stuck with unless there is something that you left out of the question. The reason is that the Will County Court finalized the final decree, stipulation or whatever the courts call the final document that embraces all of the terms of the divorce, and barring some major change, which I do not see in your case, that court retains jurisdiction over enforcement of its own order.
Don't waste your time with the small claims court, they'll just dismiss it.
If Illinois has some quirky jurisdictional rule of civil procedure or law that allows small claims court to enforce marital decrees, I would be very surprised.