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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
We would like to commend your keenness on learning the Quran and studying Islamic knowledge and striving in instilling these values in your children. May Allaah reward you generously and grant you what you wish for.
Firstly, we advise you to supplicate Allaah, The Exalted, to facilitate your affairs and help you convince your husband to approve your going to Quran memorization classes along with your children. The husband and wife should resort to dialogue and try to reach a mutual understanding in such matters. You should also consider the possible reasons for his refusal; perhaps his refusal is due to his fear for your safety or the like, and in this case you should keenly set his mind at ease and help him ensure your safety. The important thing is to reach a mutual understanding on the matter.
If he is convinced, all praise be to Allaah; otherwise, you should know that it is impermissible for you to leave your house without the permission of your husband unless you are going out of the house for the purpose of seeking knowledge the acquisition of which is deemed an individual obligation and there is no other way to acquire this knowledge except by going out of your house. The Islamic knowledge that is classified as an individual obligation on each and every Muslim is the knowledge that is needed for the Muslim to hold a sound Islamic creed and perform valid acts of worship. Memorizing the Quran is not obligatory. Ibn Muflih wrote, "Scholars have reached a scholarly consensus that it is recommended to memorize the whole Quran..." [Al-Aadaab Ash-Shar‘iyyah]
For more benefit, please refer to fatwa 85512.
Hence, memorizing the Quran is recommended while your obedience to your husband is obligatory; a recommended act cannot be given precedence over an obligatory duty. You can seek other ways of memorizing the Quran and acquiring knowledge that does not constitute disobedience to your husband; you may ask a female friend to help you memorize the Quran or use reliable internet programs for instance.
The same applies to the children. It is obligatory to teach the children the needed Islamic knowledge that enables them to hold a sound Islamic creed and perform valid acts of worship. Ibn Muflih wrote, "According to the Shaafi‘i school, it is obligatory on the father, and all other guardians, to teach his child what he needs for his religion. Ash-Shaafi‘i and his companions held that the mother takes this responsibility in the absence of the father. This is deduced from the report on the authority of ‘Abdullaah ibn ‘Umar as he said, 'Just as you have a duty towards your parent, you also have a duty towards your child.' [Ahmad and Muslim]." [Al-Furoo']
If the father refused to provide someone to teach them the required Islamic knowledge and there are no other ways to acquire it except by going to the Islamic center or the like, then the father is not legislatively entitled to forbid them from going there. It can also be fairly deduced that there is no harm in taking them to these Islamic centers without the father's knowledge if he has no valid reason for his refusal even if that knowledge is not obligatory like memorizing the Quran; as it is not becoming of a Muslim parent to prevent his children from memorizing the Quran.
Lastly, there is no doubt that if you can resolve the matter without disputes between you and your husband, then this is better. We emphasize that it is important to try to reach a mutual understanding with your husband and also use other ways to teach yourself and your children about Islam and thus accomplish your objective and maintain the stability of your family.
Allaah knows best.