Who has more right to custody, the father or the mother, and does the children's maintenance obligation fall away from the father if the mother insists on taking them with her?

"The issue of who has the greater right to custody and the circumstances under which it is forfeited is a matter of scholarly disagreement. A fatwa might not be very helpful in this regard, and it is necessary to refer to the Sharia court to determine the best interest of the children regarding with whom they should stay. As for the children's maintenance, it is not forfeited by the mother's insistence on keeping them with her, as there is no necessary correlation between maintenance and custody."