Thanks so much for your question. You may be able to look elsewhere in previous “Ask Abdu” sessions here on connect for my responses to questions on the general approaches to Muslims. They may be of some help to you.
Your question seems a bit more geared to reaching a Muslim family member, which can be a bit trickier given the relational dynamics. I’ve often said that one of the best inroads to great conversations about Jesus is relationship. Ironically, relationships can also be the greatest barriers to meaningful conversations. In parent-child interactions, there is sometimes a rebelliousness or something milder like a fear of being told “I told you so” or “I knew you’d come around” that shuts the ears and hearts of sons and daughters. I have no way of knowing if that’s happening with your situation, but it is something to be aware of as a relational undercurrent.
Another interpersonal issue is the cost of coming to Christ. With your daughter’s current stage of life, it would be very difficult to give her life to Jesus not only because of Islamic prohibitions, but also because it would cause strife in her marital and parental relationships. That doesn’t mean that you shouldn’t share, it just means that she and her family may be a lot more resistant to logic, facts, and the like.
As well, it seems to me like she her romantic feelings for her husband may have contributed to her becoming a Muslim. Now, it’s important that we not commit a logical fallacy here. Just because she may have become a Muslim due to her romantic feelings doesn’t necessarily mean that Islam is false. But it is important to consider those motivations for becoming a Muslim because they can easily contribute to a person staying a Muslim .
Now to the substance of your question. You are quite right that Islam seems to borrow heavily from (and in some instances outright copy) the OT. A friend of mine, Dr. Mark Durie, has recently published a very good (but very academic) book on this entitled “The Qur’an and its Biblical Reflexes.” You can find it here if you’re interested. Now, when you point this out, she may respond by saying, “Of course, Islam is the progressive revelation of God, bringing us back to the true monotheism of Noah, Abraham, Moses, and Jesus, all of whom obeyed the law as originally revealed.” That’s where you can actually find something that the Qur’an borrows that inadvertently points to Jesus.
Your daughter and her family likely celebrated the Muslim holiday of Al-Adha. This holiday commemorates Abraham’s obedience to God in being willing got sacrifice his son at God’s command. This story is found in Sura 37:100-107. What is interesting is a detail at the end. When God stops Abraham from killing his son, the Qur’an mentions that Abraham’s son is “ransomed with a momentous sacrifice” (v. 107). This obviously borrows from the biblical account in Genesis 22, in which Abraham’s son (who it is isn’t important for the discussion) is replaced by a ram caught in a thicket. The question for Muslims is this - why? Why does Abraham’s son need to be ransomed at all? Why didn’t Abraham sacrifice one of his one animals in his son’s place? The Qur’an doesn’t fill in the details to give us a reason. But the Bible does. When his son asked him where the sacrifice was going to come from, Abraham told him “God will provide.” This is a prophecy of the ultimate sacrifice that God would provide in his Son. You see, the Qur’an borrowed “too much” from the Bible and at least implicitly acknowledged that someone as righteous as Abraham’s son still needs to be ransomed with a sacrifice. But Islam doesn’t provide any such ultimate ransom. But the Bible tells us that God provided through his son.
I pray that an opportunity arises for you to ask her what Al-Adha is all about so that you can point some of this out to her. May the Holy Spirit guide you!