What are the rulings regarding the ‘aqiqah, and is it obligatory upon the father or the mother, and is it permissible for the father to give money to the mother for her to slaughter the ‘aqiqah from her own money?

The one who is responsible for the 'aqeeqah is the one burdened with the child's expenses. No one else should perform it without his permission. Therefore, if the father insists that no one else should slaughter an 'aqeeqah for his daughter, then it is not permissible for anyone else to perform it, not even the mother. The mother must seek permission from the father to perform the 'aqeeqah for their daughter. If he gives permission, then her vow is valid and must be fulfilled. If he does not give permission, then her vow is not binding, and no expiation is required for not fulfilling it. This applies if she intended the 'aqeeqah in its technical, religious sense. However, if she merely intended slaughtering an animal as an act of drawing closer to Allah and out of gratitude to Him, then she must fulfill it, and any slaughter for the sake of Allah would suffice. If the husband grants money to his wife and she takes possession of it, then it is permissible for her to use it to perform the 'aqeeqah for their daughter.