Odd situation

From a woman's POV - I completely agree with you guys!  : )  I think a lot of people are like that little monkey in the tree - they don't want to let go of one vine until they are certain the other vine is going to support them.  THEN there is also the possibility that as odd as it may seem - your wife may still have feelings for you.  She is conflicted.  HOWEVER - she can't do this to you unless you let her. 
I agree that you have to stop the madness : 0 and let her know that while you see she is trying to reach out - she has made it clear to you that you are no longer a couple --- or something like that. 
My husband just offered yesterday to help out with this huge project in the house that he LEFT behind when he left me.  I looked at him and said - thanks but no.  I know I am in this alone and I will handle it alone.  There was no way I was going to let him into "my" house and have him do a day of charity. 
IF you want to try to save your marriage AND your wife is willing to try - then I agree with Barkley --- seek therapy as singles and then when your therapists feel you are ready - move into couple's therapy.  Regardless it would be really good for you (and your kids BTW) to see someone you can talk to. 
I wanted to try to save mine - but my husband was gone, gone, gone.
Best of luck

I agree with both Barkley and Blee, this is toxic and it's got to stop.  She told me the other day that she can't even think of her life without me in it.   I just told her that I refuse to be her friend and she's got to make a choice.  What's going on right now is not living life, it's being a puppet for someone else.  I have to pick up my kids today from her and I am walking away from her.  I've been thinking about this all weekend long and I honestly don't care at this point if she follows me or doesn't.  I just want her to really leave me alone and move on in the awful direction she's admitted to choosing.

My wife is the queen of manipulation, Your wife may have been trained by my wife, like some sort of apprentice (or sith lord).  
On serious side, I am learning to deal with a very manipiulative wife as well, believe me you are not alone.
you have to realize that you are enableing her to do this to you (as I am starting to realize with mine).  I agree with Barkley, you need to gather up what dignity you have left and separate yourself from this toxic (convenient for her)relationship.  This will be her moment of truth and she will show her true colors.  The message should be clear that you are no longer going to be strung along, and that you are not afraid to move on.  Take control of your life with confidence.  The first steps are the hardest, but once you get the space you need to think clearly, you will see that you can move on with your life.  It is a long road ahead and she will (like my wife is doing) attempt to play games with you and at your expense.  For me, I am learning that the games she is playing are always changing, but they all amount to a form of manipulation or control.  I just have to have the sense enough to recognize when it's happening....she is subtle, and so very gooooood at it.  I Hope the best for your situation.

It sounds like she is making sure she still has you if the other relationship does not work out.  You need to go on with your life and let her see you are not waiting around on her anymore.  She will be forced to make a decision if you do it for her. Let her see what it is like to not have you around anymore.  You both should seek counseling together and seperately to be able to move on and not stay in "limbo" like this.