She probably wasn't addicted to the antidepressant, even if she was physically dependent on it. The lying and denial are absolutely normal for alcoholics. I would suggest leaving the sleuthing alone. You know what she's doing, she's not going to admit it, and the battle of wills over that can make things worse than the drinking does in and of itself.
If you aren't already going to Al-Anon, this might be a great time to start. You don't have to decide anything right now, and getting your own head clear will be invaluable when the time comes for you to make a decision. In the meantime, learning about detachment and boundaries can help make life more bearable.