Is it permissible to leave one's job to devote oneself to the home, husband, and memorization of the Qur'an, knowing that the husband desires his wife to work, that their financial situation is moderate, and that there is mixing at work and crowded and bothersome transportation?

It is not permissible to continue working in a mixed-gender environment that requires using mixed-gender transportation if the woman is not in dire need of it. Mixing with men is a serious matter, and its harms are great. Whoever fears Allah, He will make for him a way out and provide for him from where he does not expect. Your mother-in-law has no right to interfere in your personal affairs, and it is not permissible to appease her at the expense of religion and honor. A woman can look for another job with a lower salary that preserves her religiosity.