Should a woman stay home and not work to take care of the children?
I find your question perplexing because I don't know of a greater work or a more difficult work than that of raising children. One of the tasks assigned by God to women is that of home management. "That they admonish the young women to love their husbands, to love their children, to be discreet, chaste, homemakers, good, obedient to their own husbands, that the word of God may not be blasphemed" (Titus 2:4-5). The importance of this duty is seen in the final phrase. Women are to do these things so that the word of God may not be blasphemed. In another letter, Paul express it in this manner, "Therefore I desire that the younger widows marry, bear children, manage the house, give no opportunity to the adversary to speak reproachfully" (I Timothy 5:14).
The rise of feminism has caused many people to have a distorted view of what home managment entails. However, we can see it described at its fullest in Proverbs 31:10-31 in the description of the excellent wife. Just as a husband is responsible for managing the incoming funds on which a family operates, the wife is responsible for managing the outflow of these funds. Money is not a limitless resource; it must be used wisely to gain the best value for what is spent. Like a merchant who searches out the best bargains in order to reap the greatest gains, so must a wife search out bargains. "She is like the merchant ships, she brings her food from afar" (Proverbs 31:14). In getting the most out of every dollar, a wife might use the produce of her household to produce additional funds. "She considers a field and buys it; from her profits she plants a vineyard. She girds herself with strength, and strengthens her arms. She perceives that her merchandise is good, and her lamp does not go out by night. ... She makes linen garments and sells them, and supplies sashes for the merchants" (Proverbs 31:16-18, 24).
Just as a husband should help his wife in the accomplishment of her duties in caring for the household, a wife may make use of her abilities and talents to help her husband in fulfilling his duties of supporting the family. However, neither should get so wrapped up in doing the other's duty that they begin to neglect their own responsibilities. Each should view the aid they receive as a kindness and not a requirement.
A lot of work goes into managing a home. "She watches over the ways of her household, and does not eat the bread of idleness" (Proverbs 31:27). A wife plans the meals and assigns tasks to members of the household. "She also rises while it is yet night, and provides food for her household, and a portion for her maidservants" (Proverbs 31:15). She monitors the family's funds. "She perceives that her merchandise is good, and her lamp does not go out by night" (Proverbs 31:18). She provides clothing for her family and sees to the teaching of her children. "She is not afraid of snow for her household, for all her household is clothed with scarlet. She makes tapestry for herself; her clothing is fine linen and purple. ... She opens her mouth with wisdom, and on her tongue is the law of kindness" (Proverbs 31:21-22, 26). Surely none of these tasks are meaningless nor menial!