Defining a time for the father to visit his child who is in his mother’s custody
Question

Does the judge have the right to rule that the father may visit his children on only one day of the week? Is one day sufficient to satisfy the father’s longing to see his children? Is this verdict based on the Sunnah of the Prophet or a command of Allah, may He be exalted?
Praise be to Allah.Firstly:
The father has the right to visit his child who is in his mother’s custody, according to scholarly consensus.
It says in al-Mawsu‘ah al-Fiqhiyyah al-Kuwaitiyyah (17/317):
Both parents of the child who is in custody, if they have separated, have the right to see him and visit him. This is a matter concerning which there is consensus among the jurists, but they differ with regard to some of the details. End quote.
It says in Fatawa al-Lajnah ad-Da’imah li’l-Buhuth al-‘Ilmiyyah wa’l-Ifta’ (21/205):
If the wife has left the marital home or the spouses are separated by divorce, for example, and they have one or more children together, then according to Islamic teachings it is not permissible for one of them to prevent the other from seeing and visiting their child. If their child is in the mother’s custody, for example, it is not permissible for her to prevent his father from seeing him and visiting him, because Allah, may He be glorified, has enjoined upholding ties of kinship, as He, may He be exalted, says (interpretation of the meaning):
{ Worship Allah and associate nothing with Him, and to parents do good, and to relatives …} [an-Nisa’ 4:36].
And according to the hadith: “Whoever separates a mother and her child, Allah will separate him from his loved ones on the Day of Resurrection.”
Permanent Committee for Academic Research and Ifta’
Bakr Abu Zayd, Salih al-Fawzan, ‘Abdullah ibn Ghadyan, ‘Abd al-‘Aziz ibn ‘Abdillah Al ash-Shaykh. End quote.
Secondly:
There is no specific text from the Prophet (blessings and peace of Allah be upon him) with regard to defining the duration of visits to see the child. Rather it is a matter to be worked out by jurists. For more information, please see: al-Mawsu‘ah al-Fiqhiyyah al-Kuwaitiyyah (17/317-318).
From these different views, it seems that the scholars pay attention to the following when working out times for seeing the child:

The best interests of the child in question
Visits should be on a reasonable basis, so that the parent who has custody will not be harmed.

Therefore each case should be worked out on its own merits, according to the best interests of the child, the circumstances of the parent who has custody, and the circumstances of the parent who is asking to visit the child, in order to put an end to disputes that often occur between the parents because of these visits.
If the shar‘i court decides on a time and duration for visits, then they must have worked it out on the basis of what is thought most likely to serve everybody’s interests. If the father thinks that the time allocated is unfair, then he must lodge an appeal so that his case may be re-examined.
And Allah knows best.