Your wife indicated to you that she wanted to try to reconcile. Now its up to you to set the rules for what your new relationship may or may not look like.
Is it okay for her to see other people when you get back together? If not then you need to make it clear to her that you are not open to working on the relationship if she has any contact with the OM. Let her know you understand how difficult breaking all contact with him might be for her, but its non-negotiable if she wants to give your marriage a shot. She needs to prove to you that she is invested in your marriage.
What are you saying to her if you allow her to ride the fence, saying one thing, and doing the opposite?
I would also suggest that you and her read After the Affair - if you can do it together and discuss the chapters as you read them, it could help in the healing.
