My suspicions are based on ex's facebook posts mentioning new husband and comments our children made about having a step-sister. Kids let that slip; they said she asked them not to tell me.
This should be enough to get started with a lawyer filing a motion, I would think. In many states marriage certificates are public information. Don't know about IL in particular, but I am certain a decent lawyer should be able to figure this one out. Also think going that route will be a lot less expensive than hiring a PI.
Whenever you think divorce is bad, remember there are worse things than divorce.