Can a man take his wife back after divorcing her three separate times, taking into account the circumstances of anger and drug abuse in some of those divorces, and his desire to preserve his family and raise his children?

If you divorced your wife with a triple divorce, intentionally and while fully conscious, then the three divorces have taken effect. Anger, illness, or intoxication are not considered valid excuses as long as you were fully conscious. Thus, your wife has become irrevocably divorced from you (baynunah kubra), and you cannot take her back unless she marries another man, and then he divorces her or dies, and her 'iddah (waiting period) expires. It is advisable to present the matter to a Sharia court or a reliable scholar.