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 ʻalayhi wa sallam, is His slave and Messenger.
We ask Allaah Almighty to generously reward you for what you are doing for your wife's daughter. Your wife should help you in this regard; she is entrusted with raising her daughter and should instill the correct Islamic beliefs and manners in her heart and mind. Allaah, The Exalted, says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones, over which are (appointed) angels, harsh and severe; they do not disobey Allaah in what He commands them but do what they are commanded.} [Quran 66:6] The righteous predecessors said that “protect” in the verse means to teach them and discipline them. Ibn ʻUmar reported that the Prophet, sallallaahu ʻalayhi wa sallam, said, “...and the woman is a guardian in her husband's house and is responsible for her subjects...” [Al-Bukhari and Muslim]
You did well by being keen that your step-daughter observes the hijab and keeps away from potential sources of fitnah (temptation) for her. This falls under the heading of enjoining good and forbidding evil, an obligation that every Muslim is enjoined to observe. Allaah, The Exalted, says (what means): {And let there be (arising) from you a nation inviting to (all that is) good, enjoining what is right and forbidding what is wrong, and those will be the successful.} [Quran 3:104] Abu Saʻeed Al-Khudri narrated that the Prophet, sallallaahu ʻalayhi wa sallam, said, “Whoever among you sees an evil, then he should change it with his hand; if he cannot, then with his tongue; and if he cannot, then with his heart, and that is the weakest of faith.” [Muslim]
She should not be left vulnerable to the Devil; rather, she should be aided to adhere to the straight path and advised in this regard. We advise you to treat her kindly, respect her intellect, and show her the beauty of Islam, especially through learning the biography of the Prophet, sallallaahu ʻalayhi wa sallam, and his virtues. Moreover, you and her mother should be a good example for her, hoping for the rewards of your Lord. The Prophet, sallallaahu ʻalayhi wa sallam, said to ʻAli when he sent him to Yemen, “By Allaah, if a single person is guided by Allaah through you, it will be better for you than a whole lot of red camels (meaning the best kinds of wealth).” [Al-Bukhari and Muslim]
Allaah knows best.