The Rights of a Christian or Jewish Mother

Salam. I have a question regarding the rights of a christian or jewish mother ( I will use the abbreviation POB from now on for simplicities sake) over her muslim children after she gets divorced from the muslim father. As I understand the children can stay with their mother until they are seven if there is no threat of her trying to convert them. After that they must go stay with the father to preserve their muslim character. However, does the POB mother still have visitation rights? If so are those visitation rights equivalent to the rights she would have if she were muslim?Also I understand once the children are mature they can choose whichever parent they want to stay with. Once the child reaches this age can he/she decide to stay with the POB mother? I would assume that by then they would be grounded in islam enough to make a good decision. Plus, everyone wants to stay with the mother at some point even. If they decide to stay with the father does the mother still have visitation rights? Also does the POB mother have the right to be consulted considering major and minor decisions about the child.I have asked these questions because I am shocked when I read stories of muslim people who abduct their children and never let the mother see them and be a part of their lives, just because she happens to be POB or some other religion. The mothers love is such a special love that it cannot be replaced by any other female relative of the family. Many of these people say that their actions are justified by islam, but I fail to understand this. Why would Islam allow a POB woman to be the head of a muslim household and be the mother of muslim children, and then, in the unfortunate case of divorce, tell the family to throw her out of their lives?