The story of the Amalekites is a really interesting one . I find the theory that they are the same group as the Amlicites from Alma 2 to be highly persuasive. I also think that it is highly likely that they were linked to the descendants of Mulek because they are described as King men and it seems that they are upset by their loss of traditional power. This means that they nursed a deep grievance which festered into anger. And they are also followers it Nehor who reject the need for Christ and are willing to use violence to cause political change.
This was a dangerous combination. After they joined the Lamanites they continued to rally against the perceived injustice of the loss of power. And unlike the Lamanites, these grievence were still fresh and very raw. So they were a powerful force motivating towards warfare.
It seems to me that naming their great city Jerusalem was really a political statement against the Nephites. The Nephites taught that Jerualem had been destroyed because of wickedness and that God had spared them by inspiring Lehi to leave. But the Amalekites and Lamanites has a counter narrative where they saw Jerusalem as a symbol of purity and righteousness and sorrows over the fact that they were led out by a visionary man. For them, Jerusalem was a symbol of everything that was wrong with the Nephites.