Originally Posted by Roasted Cashew
The term "Children of Israel" DOES apply to Muslims. Wherever instances of other peoples are mentioned, in any story of any Prophet of Allah, or a situation, these are all meant to address the Muslims. The Qur'an addresses all of mankind, don't get me wrong. But all of these other groups are intended for Muslims as well.
Here is why. Consider the following Hadith:
Narrated Abu Sa'id Al-Khudri: The Prophet said, "You will follow the ways of those nations who were before you, span by span and cubit by cubit (i.e., inch by inch) so much so that even if they entered a hole of a mastigure, you would follow them." We said, "O Allah's Apostle! (Do you mean) the Jews and the Christians?" He said, "Whom else?" (Book #92, Hadith #422)
Thus, every verse about the past nations is meant as a warning for the Muslims as well. That is why when it is addressed to past nations who did wrong, then the Muslims are meant as well. Thus, the term "Children of Israel", is in fact saying "O you Muslims who are like the Jews!". There was a letter by Hazrat Muhammad ibn Abdul Wahhab (ra), where he explained how the Muslims have become like Jews in many ways during his time. That wasn't very far from now. And if you have read Surah Al Fatiha, then you know that the last verse speaks about the Jews and Christians according to commentators. We are always praying to not be like the Jews who were deserving of Divine punishment, and to not be like the Christians who went astray and became idolators. The threat of Muslims becoming idolators is very real and is something which would happen in the very last age:
Narrated Abu Huraira: Allah's Apostle said, "The Hour will not be established till the buttocks of the women of the tribe of Daus move while going round Dhi-al-Khalasa." Dhi-al-Khalasa was the idol of the Daus tribe which they used to worship in the Pre Islamic Period of ignorance. (Book #88, Hadith #232)
So when there is warning to anyone about not becoming idolators after believing, or in any other situation, then that warning is very much meant for us Muslims as well. There is always a looking threat to every Muslim of becoming one who associates partners with God. It is difficult in more than one way.
So to answer your question, I suggest you look at "A Letter on the Censure of Taqleed" by Hazrat Muhammad ibn Abdul Wahhab (ra). This letter is a very informative one. It will make more clear to you why the Qur'an addresses "Children of Israel" and still refers to the Muslims. Although, the Hadith I gave you should be fine.
Another interesting point here is that in a university course I took, my professor explained the encounter between Muslims and Jews (that was the course actually), and she made a comparison between the history of the religion of Judaism and Islam, and how they both developed over time with regards to their method of interpreting their religion and the religious canon. There is a striking similarity between both of them, and the way they have both developed is parallel. Thus, Muslims have, in fact, been very much like Jews in a lot of ways. I am not saying literally. But the way in which our histories have developed, they are similar. This is not what I made up, but this was a University of Toronto professor. I wouldn't dispute that. Neither would I dispute a reputable scholar like Hazrat Muhammad bin Abdul Wahhab (ra) in his striking comparisons using the Holy Qur'an.