I have experienced a very similar situation. My husband cheated on me. I knew something wasn't quite right and I gradually gathered evidence and worked out exactly what was going on. There was a lot to sort out in my head and I experienced a whole range of emotions; I was hurt, angry and confused, but in a way it was a relief to be dealing with reality rather than lies and suspicions. I gave myself time to think things through before I confronted my husband. I could tell that he cared very much about the other woman (C) and it was clear that she cared for him too.
I told my husband that if there was to be any chance of working things out I needed him to tell me the whole truth about everything that had happened. It was hard to hear some of it but it helped me to understand why it had happened and I think it made him realise how much he had hurt me. I decided to accept the relationship if he could promise absolute honesty from that point onwards. That was three years ago, it didn't work out as I expected, C and I have become very close and what I thought would be a V is much more like a triangle, each of us is very important to the other two and each of us plays an important part in making the relationship work and supporting the other two.
To answer your questions I think you need to change the way you are thinking about this situation. It is not all about you, there are three people involved in this and all their needs need to be met not just yours. So far doing it your way has achieved an emotional mess and you are very lucky that you have not lost both of these women. Don't 'set something up for the weekend' give each woman the email address and phone number of the other then take a back seat and leave them to contact each other and get to know each other in their own way and their own time. if anything more is ever going to happen they need to become friends and build up trust in each other and you need to give them space to do that. The worse thing you could do is to try to rush things. Your wife will need lots of time and reassurance from you, so for now devote most of your time and effort to your wife and remember that U has feelings too and she will also need reassurance. Most important of all no more lies!