Family can be the best motivator
I have an interesting suggestion that might combine both of your options as far as telling your wife and kids. I agree with other people that letting your actions speak louder than words is a powerful thing. Especially since your wife and kids WILL notice that you are having much more fun living life and being active. Focusing on family life and being a part of your kids is important. They'll grow up fast, so you need to quit and start spending time with them before they go off to college and become adults themselves.
Perhaps setting a goal for yourself such as sobriety for 6 months then reward yourself by telling your wife. That way you can tell her that you are actively fighting the problem and have been successful for this amount of time. She'll be impressed.
With your kids, it depends on how mature they are. Perhaps saving the alcohol discussion for when your kids are about 15-16 is a good idea. They are going to be dealing with it in high school, all their friends are going to parties and getting drunk/experimenting with drugs. Sitting down with them and having a good chat about drugs and alcohol can be a positive force for them. You certainly don't want them succumbing to alcoholism. One of my friends in college absolutely refused to have type of alcoholic drink because her grandfather had an alcohol problem. Her parents talked to her about the dangers of alcohol, and she had resolutely made the decision to never taste the stuff. If you intellectually discuss alcohol and its consequences with your kids, I promise you that your voice will be in the back of their minds at the next party. Telling them that you personally have a problem with alcohol may drive the point home even further, but that is really a decision for you to make. You have to be dedicated to sobriety before really discussing this with them. Otherwise its like the blind leading the blind.
When you look at your life, the greatest happinesses are family happinesses. ~Joyce Brothers
I want to wish you the best of luck in your endeavors. Stick with and keep all your motivating factors in mind. I'm headed down the same journey.