Early in the second part, Chapter Women of the Quran describes obedience to God, the Prophet Muhammad, and “holders of authority from amongst you” (‘ulil amri minkum). Imam alBaqir and Imam Jafar alSadiq interpret that last phrase to refer to the Imam of the Time, the holder of religious authority, even though the word can equally describe holders of secular authority (politicians, law enforcement, parents, teachers, etc) as noted by Qadi Nu'man. The “from you” clarifier (minkum) further complicates the interpretation: that descriptor would be incompatible with divinity commonly ascribed to the Imam. You can read more about that here.
The next verse in the Du'a comes from Chapter Test, in the Quran. This chapter talks about the conflict between God sending down a message and people not believing it. The verse in the Du'a refers to the power of God, and how he's placed his authority into the Present Imam (إِمَامٍ مُّبِينٍ), more specifically: he's listed everything for the Imam. This imagery also reflects a similar story about Adam, the first man. With this placement of knowledge of all things juxtaposed with the earlier verse about obeying authority, the consensus is that obedience to the Imam is akin to obedience to God.
One of the defining characteristics of the afterlife in Islam is that it is an "abode of peace" (دار السلام); those who enter are greeted with peace ("asSalam alaikum") and it's filled with kindness. While people seek to create peace on earth, even incorporating the greeting into daily life, there's an understanding that true, all-encompassing peace can only come from God. So, the second part of Du'a expresses that God is peace, and asks for peace from God.
ya ali madad
In the second part of the Du'a, as well as in the common Ismaili greeting, Imam 'Ali is asked for help. This is a point of contension for Muslims, as we've already established that help can only be sought from God. However, as demonstrated in the rest of the part, the Imam has been appointed by God to be a source of divine authority on Earth. Just like obedience to the Imam counts as obedience to God, asking help from the Imam counts as asking help from God. It's not a direct process, but it's the closest a mortal can get.
The second part of the Du'a ends with a declaration of faith: known as the Shahada. The Shahada consists of proclaiming the oneness of God, and the prophethood of Muhammad. The Ismaili Shahada also includes a proclamation that Imam 'Ali was appointed rightfully from God, reiterating the rest of this part. The current Imam is also mentioned, having filled the role of Imam, after 'Ali.