If you and your wife have been experiencing significant problems in your marriage, and she has expressed her desire for a divorce, you are likely dealing with a number of emotions. However, if you believe that your marriage can be saved and you want your wife to see this, there are some things that will possibly convince her to give the relationship another try.
Pay attention to the things your wife says she is missing in the marriage. Write them down, so you can remember and review them. Ask her if there are things you can do to remedy the problems she sees in your marriage at this point. For instance, if she needs you to be more attentive, ask for details on how you can make this happen, for example,"Do you want me to take care of the kids when I see that you're stressed?"
Start doing the things that your wife has been telling you she needs you to do. If she's been pleading with you to be more romantic, bring flowers home for no reason or hire a babysitter and plan a romantic evening for just the two of you. Don't get discouraged or angry with your wife if she doesn't respond to your gestures the way you would like right away. Show her that you have patience and are understanding of her feelings.
Take the initiative to do things that may help to repair your marriage. Make the call to the marriage counselor and set up an appointment. Arrange for you and your wife to go on a marriage retreat without asking her to make any of the trip plans.
Communicate with your partner often -- about things that don't concern your obligations to one another or your children. For instance, send her an email telling her that you miss her and sincerely hope that the marriage can be reconciled or leave her a note that describes the personality traits that you admire about her. Tell your wife how you feel about the problems in the marriage as well, so the two of you can get a better understanding of what it will take to make things better.