As a primary whois going through this, I felt like you were writing my story except that the other is not willing to stop and be just friends, she wants him to herself and is actively pursuing him...anyways back to topic. Be there for you wife. Let her know/feel how much you love her. Understand the meeting will be hard on her regardless of the impression he puts off at the time. After the meeting. Be present for your wife, don't run of to support Rita. Your wife may be fine or appear to be and then something may trigger and she will need understanding not anger or isolation. If at anytime she is not comfortable or ready let her back out and don't get frustrated or mad. Never allow Rita or any other secondary talk down to your wife, stick up for her, if they start to or she feels like they are. Since she has expressed non approval at the beginning but is willing to meet now doesn't guarantee se won't have a ton of emotions later.
In my case hearing that my husband loves her and feels like he is getting his heart torn in 2 is harder than knowing they had sex.
Best of luck and hope to hear a good outcome for all