Does the Bible actually say that mothers should not work outside of the home?
First, Titus 2:5 does not specifically teach that just mothers are to be "keepers at home," but it is applied to all young women.
The phrase "keepers at home" (KJV) is from the greek word "Oijkourgov▀." (i.e. "oikourgos.") This is combination of two greek words: oikos, meaning "home" and urgos, translated "worker." "Urgos" is derived from the root word "ergon" which means "work," "employment," or "task." (Vines Expository Dictionary of NT Words). Robertson notes that the older manuscripts contain the word "oikourgos," while some newer ones transliterate 'urgos" to "ouros" i.e. "keeper," - which more accurately means someone who is watching over something or being a guardian.
Thus, a woman's work, employment, or task is to be working in, and watching over the home. John Gill's commentary on Titus states that the Jews taught that is what is meant by being the "helpmeet" of her husband: "that while he is abroad about his business, she is (tybb tbvwy) , "sitting at home", and keeping his house."
How is the word of God blasphemed if this is not followed? I have often wondered where Adam was when Eve was being tempted. The bible teaches that the woman was more susceptible to the temptations of the devil. It seems that she got into lengthy discussion about God's will over the forbidden fruit and Adam had no input into that conversation. The curse that they brought upon themselves was that Adam was to have toil in his labor in earning a living, and Eve was to have pain in child birth and struggle against the urge to usurp her husband's authority over her. While Eve's temptation was distinctly limited to her female characteristics, it can also be reasonably concluded that Adam's toil in providing for his family is representative that it is the man who is to earn the living.
Matthew Henry notes in his commentary on Titus 2:5 that Dinah was sexually defiled when she went out to visit "the daughters of the land" (Genesis 34:1); not to mention the tragedy that followed involving Simeon and Levi avenging their sister's defilement.
Today, the divorce rate in this country is said to be about 50%. Some marriage counselors have reported that adulterous relationships occur mostly between people who meet each other through their jobs. Likewise, it is estimated that women hold approximately 50% of the jobs in the workforce. Are these statistics just coincidental? How many lives have been ruined by two co-workers of the opposite sex falling into temptation? How many lives and businesses have been ruined by sexual harassment in the work place? How many pastors have run off with their church secretary's? How is a person to obey the command to "flee immorality" if they are enduring temptation at work for another person? Must they quit their job?
Proverbs 31 describes the "excellent wife" as one who "looks well to the ways of her household." All of her work and enterprise, and even running a small home business, are all done in the home. I believe this is what is meant in Titus 2:6 when it says that a woman must be subject to her "own husband." I used to ask "well, who else's husband would she be subject to?" However, a woman at work in the workforce is subject to another authority, her employer - who may be a male supervisor. A woman in an employer/employee relationship is under authorities that God has not enjoined her to.