Your wife answered you truthfully. She does not know what what she wants. Read between the lines. She also told you she is selfish, and is not very concerned about what you want, or for that matter her kids. Its all about what she wants!
I am sick and tired of alcoholism being an excuse for bad behavior. The fact is, we do not have to tolerate their abuse.
My guess is you are doing all the work in your family. Financially, emotionally, caring for your children. Your wife is only concerned about herself and her needs. If she cheated in the past, she will most likely do it again in the future. Her membership in AA will give her ample chances to have another affair.....drunks love a drunk!
I was married 19 years too. We have two beautiful kids. I miss my old life and I miss my wife. But the reality is what it is. The person I married no longer exists and my marriage is over. The good news is...the madness of living with the alcoholic is over. My kids are safe. My heart can start to heal. I have a chance now to find a new love, one who can return my love. The chance for a new life.
Life is short....you and your kids deserve to be happy.