Depending upon the situation, mothers should get custody of children after a divorce. There is nothing like "mommy" and there are no substitutes. If either parent is abusive, then the other parent should win custody. Ideally, both father and mother share custody of children in equal measure. Unless the mother is completely derelict, she should get at least some physical custody of biological children.
A mother may not be the best parent for a child if the parents are getting a divorce. If she doesn't have the ability to pay for all the child's needs, or perhaps has criminal convictions I would argue the father is the most fit parent. If neither parent is fit, then the child should be given to relatives willing to take it in.