It is a quandary, but the way to rebuild intimacy is to first rebuild ATTRACTION. The challenge is, a key part of rebuilding attraction is the re-establishment of RESPECT, and a woman won't respect a man who knows she's cheating and he isn't calling her on it.
It's a fine needle to thread.
What were the consequences -- if any -- to her continuing to have (she claimed) non-intimate contact with this man? That was probably a huge test for you, and I suspect she's thinking "Sphew -- Mike didn't do anything about that, other than seem upset."