This verse demonstrates some of the detail that is missing from our account. This is the first time we learn of children of Amulon being among those who arrive in Zarahemla. Not only is this the first time we are made aware of them, Mormon neglects to tell us whether they arrived with Limhi or Alma. While this does not make much difference in an eternal scheme, it is still an interesting question.
If these children of Amulon came with Alma they would surely be the children of Amulon and the priest's union with the Lamanite women. Had any previous children been with Alma, surely that would have been a sufficiently significant reunion that it would have been mentioned - or at least those former children would have played some role of mediation, either lobbying for their fathers or for Alma whom they would have followed. We hear of none of this.
The second reason for seeing these children of Amulon and his brethren as the abandoned children fathered prior to the priests' escape is that children born of the union with the Lamanite women would have to be quite young, probably younger than a year, two at the most. Such children would certainly not be making informed decisions about their declared lineage.
Thus the probability is that these children of Amulon and his brethren were those who had already been rejected by their fathers. When they learn that their fathers had not only abandoned them and their mothers, but completely forsaken their former families to create new ones with the Lamanite women, the children may be seen as having sufficient motive to reject their lineal inheritance and adopt another.
Now we have the question of what they were actually doing. The Amulonites were possibly Nephite to begin with, although they could have been descendents of the Zarahemla Mulekites. In any case, their allegiance to Noah would have created some form of shift in dynastic interest. By adopting the Nephite lineage the children of Amulon not only proclaim their current political alliance, they reject any claim they might have to rule based on their father's positions. While this might appear to be a moot point since all of Limhi's people were being integrated into Nephite society, the retention of potential claims upon rulership could have created divisiveness. By declaring themselves of Nephi, they wholeheartedly accept that position, and reject any possible rulership based upon their father's former or current positions.