How do I prove my ex is living with someone so I can stop alimony?

I was ordered to pay alimony to my ex in our divorce. However, we have a cohabitation clause in our divorce decree and if she lives with someone she’s romantically involved with, I can ask a court to stop my alimony payments or reduce them. I think she’s living with her boyfriend but she’s hiding it to avoid losing the alimony. I’ve driven by his house at night and seen her car, but she still has her own apartment and she’s there sometimes too. What do I need to prove to trigger the cohabitation clause and does Illinois law allow people to hire private investigators to testify in court about cohabitation?