Jeff, If you really and truly want to try to reconcile w/your wife, do not, I repeat, do not date. If you do, you are not only involing your wife in your situation, but then a third person comes into the picture and once your wife wakes up...how are you going to deal with the third person that you, the rational one, brought in?
If you are divorcing and do not want to reconcile, that is a whole different ball of wax. Dating is freeing your spouse of any guilt that she may have about what she's doing. You are giving her the single that it's a-okay to date and you are going to do it too.
Standing for your marriage is very difficult at this time, but if you really want to try to save the marriage, please stay away from third parties and until you are absolutely certain the two of you will not reconcile....but divorce.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.