Can a woman get the child custody in case of divorce?

[Seraphina]

Salamun alaikum, brothers and sisters! I hope you're having a great Sunday!
My family is not familiar with Islam (as portrayed in the Quran), they have only seen some tv talk shows with mullahs or scholars, so you can imagine they have many misconceptions about Islam, and they often come up with questions. Yesterday in a tv show a religious clerk was stating that "prophet Muhammad pbuh said that a woman can keep the custody of her children after divorce for as long as she doesn't remarry. And, almost always a father is favored regarding the custody, because he's the one charged from God to provide provisions for his children (for his family in general). Even if the father dies, and the widow has to remarry someday, someone from father's family takes care of children (grandfathers, uncle, aunt...)".
I have some issues with this theory. First of all, I'm not a scholar but I have known Quranic laws well enough to know that this theory has no basis in it. Second of all, when God gave the divorced and widowed woman the right to remarry, He never put such conditions on them . Besides, take the verse 23 of surah Nisa: "Prohibited to you (For marriage) are:- Your mothers, daughters, sisters; father's sisters, Mother's sisters; brother's daughters, sister's daughters; foster-mothers (Who gave you suck), foster-sisters; your wives' mothers; your step-daughters under your guardianship, born of your wives to whom ye have gone in,- no prohibition if ye have not gone in;- (Those who have been) wives of your sons proceeding from your loins; and two sisters in wedlock at one and the same time, except for what is past; for Allah is Oft-forgiving, Most Merciful."(Yusuf Ali translation). How can it be forbidden for a woman to take her children with her if she remarries, when God clearly recognizes that a man can have (at least) the daughters of his wife under his guardianship?
Even if we'd take hadith and sunnah as authority (as most of muslims do), we have arguments to prove them wrong. Prophet Muhammad himself was born an orphan and his mother raised him, until she died as well. Ramla bint Abu Sufian got divorced (and later widowed) from first husband and married prophet and had her daughter living with her, when her husband was alive, and after he died. Hind bint Abu Umeya was widowed, and had three children, the fourth being born in prophet's house after he married her, and he (prophet) raised them as his own. There were attempts to take at least one of her children from her, but in the end she had them with her.
What is your view on this issue? I believe it's important for every woman to know her rights on this matter, because we never know what will tomorrow bring.
Sorry if I made it too long,
Your sister Seraphina

[Seraphina]

As-salamu alaykum,
I've been waiting for an opinion or a response on this question for so long, but since noone has an answer, and I am unable to remove it, then all I can say is I'm sorry for any possible disturbance I ever caused with my frequent posts or questions.
God bless you all,
Your sister Seraphina Rosa

[zara]

Salaam sister Seraphina,
Please don't apologise for your questions.I personally have learnt a lot from your questions an responses to others,and I would really like to know the answer to this one.
Zara

[Seraphina]

Salam wa aleyki my sister Zara,
Thank you for your kind words. I have tried my best and I will keep on trying inshallah. We are women, both you and I, and seeing the suffering of muslim women, I've come to realise that most (if not all) suffering that befell us muslim women is because we are not aware of our rights, we have no idea what our rights are. So I estimate it to be of a great importance to know our rights in any situation: in case of divorce, in case of becoming captive of war (we live in times when war can come unexpectedly), in case of inheritance/property share, and so on. We muslim women need to learn and inform ourselves of our rights, not the ones so-called mullahs impose on us, but the rights the Almighty One granted us in his divine constitution. Once we know our rights, once we know justice of God is on our side, nothing and noone can oppress us or maltreat us, no matter how powerful they are. That's why we women need to gain knowledge, the most powerful weapon of all. That's why my most frequent prayer is: "My Lord, increase me in knowledge" (20:114).
So, let's read in the name of our Lord, who created...let's read, because our Lord is the most generous, who taught by the pen that which man knew not
Your sister Serafina

[Truth Seeker]

Salaam Seraphina,

It is an interesting question and there is an indication from the Quran that if the child is under two then it may be with the mother if she is to suckle the child (Please see Joseph's article on divorce)

Also the in that article is reference to the fact that the father is to provide for the child and its well being is to be discussed under mutual consultation.
So the Mullahs indicating that the preference is the father has custody has no basis in the Quran and the verses you mention regarding marriage also proves that. The key is mutual consultation.

[Seraphina]

Salam Truthseeker,
Thank you so much for your reply, I truly appreciate it. I'd love to have brother Joseph's opinion as well, but your answer helps as well.
May God bless you,
Your sister Seraphina