What is the ruling on a woman seeking divorce without a valid reason, and does the ex-husband have the right to reclaim his children after their mother's divorce, remarriage, and childbirth with another man?

A woman is not permitted to seek a divorce without a legitimate Shar'i (Islamic legal) excuse, due to the severe warning mentioned regarding this. A divorced woman has a greater right to the custody of her children unless she remarries. If she remarries, her right to custody is forfeited and transfers to the next deserving person. If the father has the greater right to the children's custody, he may reclaim them from their mother and take them into his care and custody.