All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If the mother remarries, she loses the right of fostering her children, and the fostering in this case moves to other women who are more deserving of fostering the children after her according to the order that is mentioned by the jurists and which we have already clarified in Fatwa 84618. Therefore, saying that the fostering moves to the father is not correct.
Yes, if the child reaches the age of seven, he/she is given the choice between his/her two parents, and so, he/she stays with whomever he/she chooses. However, if the fosterer is dissolute, then he/she loses the right of fostering the children according to the most preponderant opinion of the jurists .
In addition to this, some scholars have conditioned that the father must have a female who is suitable for fostering so that he would deserve the fostering. For more benefit, please refer to Fataawa 90461 and 132638.
Finally, it should be noted that fostering and similar issues should be referred to an Islamic court or to an authority that may act on its behalf, as the matter may need some clarifications from the people involved. Also, the ruling of the judge is binding to both parties in issues of Ijtihaad (a juristic opinion on matters which are not specified in the Quran and the Sunnah). For more benefit, please refer to Fatwa 89707.
Allaah Knows best.