Is it permissible for the husband to divorce his wife who is negligent in her marital duties, and is he entitled to custody of their nine-month-old daughter?

There is no disagreement among scholars that the mother has a greater right to custody of her child who has not reached the age of seven years, as long as there is no legal impediment on her part. So, if you divorce your wife while she is breastfeeding your daughter or not breastfeeding her, and there is no impediment on her part, then she has a greater right to the custody of her daughter. The one who decides custody issues in cases of dispute is the Sharia (definition) judge. The husband is advised to pursue legitimate means of reconciliation with his wife before resorting to divorce.