All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Taking care of the children is a joint responsibility between the parents. In Sahih Al-Bukhari on the authority of Abdullah ibn Omar the messenger of Allah said: “All of you are shepherds, and every one of you is responsible for his herd. A leader is a shepherd, and he is responsible for his herd, a man is a shepherd over his family, and a woman is a shepherd over her husband’s house and his children, and she is responsible for them, a man’s slave is a shepherd over his master’s wealth, and he is responsible for it. So all of you are shepherds, and every one of you is responsible for his herd.”
Nothing prevents a woman from earning money, owning it, and spending it on what she wants of permissible things. However, if earning money requires leaving the house, then the husband’s permission is required.
It was stated in (Mawahib Al-Jalil Sharh Mukhtasar Khalil): “A man has no right to prevent his wife from trading, but he can prevent her from leaving the house.”
If your husband permits you to go out to earn lawful money or for a permissible purpose, then this is allowed, and there is nothing wrong with it, but if he does not allow you to leave the house unnecessarily, then you have no right, in this case, to go out for earning or other things that are not necessary.
You should know that a woman’s fulfillment of her obligations and her fulfillment of her husband’s rights is a great deed that leads to attaining the pleasure of Allah and His Paradise. On the authority of Abd Ar-Rahman ibn 'Awf, he said: The Messenger of Allah said: “When a woman observes the five times of prayer, fasts during Ramadan, preserves her chastity, and obeys her husband, she will be told: enter by any of the gates of Paradise you wish.” [Musnad Ahmad]
Allah knows best.