Apologizing would be a good start.

Alcohol use disorder is in the DSM 5 much like the mental illnesses you experience. It is not something one chooses (one does not decide one day to become addicted to alcohol), but one is responsible for making the choice to choose recovery. The same goes for someone with depression or other mental illnesses. One can choose to do nothing about it, or they can seek treatment in whatever form that may be (medication, therapy, exercise, meditation, etc).

Your struggles are not so different from your mother in law's. You two could be supports for each other, rather than adversaries.