Should we infer from that statement, that you've already raised the issue of her living "rent free" in court, and that the court found that she is in fact paying rent? If the issue has been decided by the court you can (subject to the time limits for filing) consider appealing or seeking reconsideration based upon facts or law that might change the court's conclusion, or moving on.
Does your provision for spousal support end if you prove cohabitation, or are you focusing on trying to prove that her expenses have gone down such that your spousal support should be modified? Has the court already decided this issue?Quoting GoingBroke18
If she's paying rent, the fact that she's in a nicer home than she was previously renting does not change the fact that she's paying rent.Quoting GoingBroke18
Even if they are commingling funds, his money is still his money.Quoting GoingBroke18

