Here is a direct source for what the Rebbe wrote about the Holocaust, showing he had the same views as Rav Shach zt”l and Rav Avigdor Miller zt”l, and what I showed his father-in-law said:
On the subject of the Holocaust, the Rebbe wrote as follows: “It is clear that ‘no evil descends from Above,’ and buried within torment and suffering is a core of exalted spiritual good. Not all human beings are able to perceive it, but it is very much there. So it is not impossible for the physical destruction of the Holocaust to be spiritually beneficial. On the contrary, it is quite possible that physical affliction is good for the spirit” (“Mada Ve’emuna,” Machon Lubavitch, 1980, Kfar Chabad).
Schneerson goes on to compare God to a surgeon who amputates a patient’s limb in order to save his life. The limb “is incurably diseased … The Holy One Blessed Be He, like the professor-surgeon…seeks the good of Israel, and indeed, all He does is done for the good…. In the spiritual sense, no harm was done, because the everlasting spirit of the Jewish people was not destroyed.”