My wife does not drive or work and has 2 other children, but has no custody. I am looking to divorce and gain custody of the child we have together. She is on depression and anxiety medicine, does this help?

Help in what? You need to discxuss this with your divorce attorney. Custody is part of the divorce decree.

At the divorce hearing her medical problems can be mentioned, but unless the medication is not dealing with her problems it won't have much bearing on the final decision. A lack of income and, depending on her living local, ready transportation might have more pull(she could not make emergency runs to the doctors... ). In the end it depends on the judge, and your own story. The system tends to favor the mother. Keep a written log of any erratic behavior, times when her situation might be considered a detriment to the childes wellbeing.