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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
When a woman is divorced, she has more right in fostering the children than her husband if she does not remarry.
The evidence about this is that a woman came to the Prophet complaining: "O Prophet of Allaah! I carried my son in my womb, I nestled him, hugged him and protected him within my arms, and I breastfed him, and his father who divorced me wants to take him away from me. Does he have the right to do so? The Prophet replied: ''You have more right in fostering your child than your husband as long as you do not remarry." [Ahmad]
So when a woman remarries, the husband fosters the child if there is no other person who has more right in fostering him. But if the wife is divorced again or her husband dies, then the scholars differed about whether or not she is entitled again for the fostering of her children. The majority of the scholars are of the view that she is entitled again for the fostering of her children, however, they differed about some minor details.
However, the correct opinion of the Hanbali school and it also the view of the Shaafi'ee school is that the mother has the right of fostering her children soon after her second husband divorces her, whether it is a revocable or irrevocable divorce without waiting for the end of her waiting period. On one hand, the Hanafi school and Al-Muzani from the Shaafi'ee school are of the view that the woman has the right to foster her children again after being divorced from the second husband, if it is an irrevocable divorce or after her waiting period ends if it is a revocable divorce.
On the other hand, the Maaliki school are of the view that the woman who is divorced by her second husband or if he dies, she has no right to foster her children again whether that is a revocable or irrevocable divorce.
In our view (in Islamweb), the most preponderant opinion is that the mother has the right of fostering her children again soon after her second husband divorces her, whether that is a revocable or irrevocable divorce, because she lost the right of fostering them when she got married, and therefore when she is again divorced, she has again the right of fostering her children.
As regards the period of visiting the children, if the court, and in your case it is the Islamic centre, did not set a special time for visiting them, then the matter depends on the customs, as there is no specific limit for the visiting of the children in Islam. If you and your ex-husband disagree about this matter, then you have to take your case to an Islamic centre to judge between you.
Allaah knows best.