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.
Zina (fornication or adultery) is a very serious matter and it is a grave major sin. Indeed, you did well by repenting but you should make this regret a sincere repentance fulfilling its conditions that we have stated in Fataawa 86527 and 87903.
If you are the one who informed your husband about having committed Zina, then you are wrong because you should have concealed your sin as the Prophet said: “All my Ummah (nation) is forgiven except those who sin openly.” [Al-Bukhari and Muslim]
If what you mentioned is true that your husband mentions that matter and humiliates you with improper words, then he is wrong as he is disobeying Allaah’s order to treat the wife kindly as Allaah Says (what means): {And live with them in kindness.}[Quran 4:19] For more benefit, please refer to Fataawa 88304 and 86618.
However, you should remind him of the fact that Allaah accepted the repentance of people who committed a graver sin than your sin and when they repented, Allaah accepted their repentance and honoured them. For example, the companions of the Prophet were upon disbelief and many of them had committed all kinds of sins, and Allaah accepted their repentance, and their previous sins did not prevent them from being raised in status. So, you should remind your husband about this and remind him also that he should fear Allaah and that it is forbidden to harm a Muslim without right.
Of course, you should do so in a nice and soft manner as Allaah may enable him to be rational and he might be deterred from this evil act. Furthermore, we advise you not to be sad due to this matter, because if you sincerely repent and Allaah accepts your repentance, then you have nothing to lose.
As regards studies, it might be understood from what you mentioned that your husband objects to this and he has the right to prevent you from doing so unless you conditioned on him to continue your studies before marriage, in which case, he is obliged to fulfill this condition.
With regard to leaving your son in the nursery, if the child is not harmed then you are not sinful for this.
Moreover, if you are not in need of this study, then it is more appropriate for you to stay at home and nurture your son as this is better for you and more secure for your religion. In addition to this, this will put an end to the dispute that you have with your husband.
Finally, it is better for you if you try to solve the problems between you and your husband only and not inform anyone about it. Involving other people may worsen the situation, so you should not inform anyone unless there is a preponderant benefit, like the need for reconciliation.
Allaah Knows best.