Is the reason for our prostrating twice in prayer that the angels prostrated a second time when they saw God's intense wrath towards Iblis after his expulsion from Paradise?

This statement is incorrect and impermissible, as it is a claim without proof. Allah the Almighty mentioned in His Book only one command to prostrate to Adam, and that the angels all prostrated except for Iblis. The prostration of the angels was to Adam, whereas our prostration in prayer is to Allah the Almighty. It has not been mentioned in the Quran or the Sunnah that Allah became extremely angry with Iblis, causing the angels to be terrified. Allah the Almighty has forbidden speaking about Him without knowledge: (He only enjoins upon you evil and immorality and that you should say about Allah that which you do not know) (Al-Baqarah/169).