I did some research on esophageal varices a year ago when my father was dying of esophageal cancer (caused by long-term heartburn, not alcoholism). I'm the type of person who wants to know all the facts so that I can prepare myself emotionally for what may lie ahead. As Mallow and FrizzyLynn have mentioned, it's a serious problem that usually indicates the presence of alcoholic liver disease. In my father's case, the cancer had spread from his esophagus to his liver (and lungs), causing the varices.
One of the problems with esophageal varices (if that is your wife's diagnosis--without speaking with the doctor in person, it's hard for you to know for sure) is that once you develop them, they tend to recur within the next 1-2 years. In healthier patients than my father, if the alcoholic is able to stop drinking there are some treatments that can help prevent a recurrence. The use of an esophageal ring was mentioned, although I don't recall exactly what that was or what it entailed.
Sending prayers for peace for you and your children, Guy, and healing prayers for your wife.