Good for you not cheating.... keep it that way or you will be fucked
I know you are in pain, but be patient and loving and keep talking. You might find that there is a glimmer of hope. Cling on to that and do as she asks for now. It sounds like she needs some time for everything to filter down. Tell her that and let her know that you intend to keep in touch with this woman and that dropping her entirely is not an option for you... you are allowed to set boundaries. Her boundary seems unreasonable for you, so don't agree to it and keep negotiating with her about what would be acceptable. You might find that you never reach a point where you can find a good agreement and might just have to compromise and be willing to let some of your needs go. That remains to be seen though, you are just starting out.
Maybe your wife would like to join here too or at the very least look at some threads on similar experiences. Here in this thread alone there are many. Lots to read. There are also some really good blogs to read also...
You are not alone. Know that. It's all very hard, but you have just begun and the future is not what you think it will be.... take a step at a time and do so with as much love and compassion/consideration as you can... that all comes back to you