Oh boy-- been there, exactly there, where you are now. More than once and I'm not proud of it. Seven days is nothing. 30 days is nothing. 90 days? That might be something. That said, every ex-drinker's story, while most are very similar, are not exactly the same. She may find it this time, but the moment you think she hasn't/isn't, trust yourself. You will be right.
I wish the best to you, but especially to your children who are always the most helpless victims of alcoholism. The damage already done to the 16 year old can't be changed, but can be treated if he/she wants it (counseling and/or Alateen). The baby may have dodged much of it up to now, but is getting old enough to really, really be ****** up by Mom. Whatever you do next must be through the lenses of protecting this child, which means you must protect you in order to protect the child. Unless she gets long term sobriety there is no possible way for your wife to be anything but a profoundly ****** mother. Protect the baby. Protect yourself so you can protect the baby.
Good luck Sir!
Cyranoak