Does she really want to/ready to make these lifestyle changes as you do?
Try to be patient, many years of poor eating habits, can take a while to change.
Being a good role model (for healthy eating & exercise) is sometimes the best thing. Also you could ask your wife,if there's something besides ice cream or junk food that could help her feel better, when she's having a bad day. Time away from the kids for a little while? A backrub? a walk to destress?
Just a few suggestions... Good luck.

It is extremely challenging to make someone change their eating habits - I had the opposite issue with my husband, he was much too thin, very underweight and I kept trying to get him to eat more. He refused to change, until finally a friend convinced him of the health benefits of eating more of the right combination of foods and he has now gained some weight and looks much better - he is no longer just skin and bone, but the point is he would not listen to me, he had to decide on his own with the help of someone he perceive to be impartial and more knowledgeable than I. I, on the other hand, am slightly overweight (20-30lbs) and struggle with maintaining healthy habits. When my husband tries to control what I eat, it only causes me to be more frustrated. We have talked about it, and he no longer does that, but I make healthier choices now because I know it is important for both of us and our long term health - and I know he worries about me, plus I feel better overall when I eat healthy and exercise. Regardless, it is my choice, one that he cannot control, and the choice has to be made for me or I wil not be able to maintain motivation in the long term. When I ask him for help, that is different than when he tries to tell me I should not eat something - that only makes me defensive and I will still eat it! Does she seem to want to change but does not have the willpower? Could she talk to someone else about it, someone neutral? Or, is she simply not motivated to change? Also, if she wants the junk food she should be able to go get it herself. Many times I asked my husband to pick up something unhealthy and would not be surprised if he said no or came home without it. If I really wanted it, I would have to go get it, and usually I was not motivated enough to inconvenience myself like that, so I did without. Then, I got used to doing without! That's the other aspect of junk food - convenience! Not sure if this helps at all, just another perspective....

One more note, neither my husband nor I holds the other responsible for our weight issues - we can help each other, but what we eat is our choice and our individual responsibility, I would not blame him for the choices I make unless he left me with no other options.