Ammon has come among a foreign and hostile people armed with a weapon. Ammon is taken as a bound captive to the king of the land of Ishmael. Yet, as noted by Brant Gardner, facing prison, torture, and possibly death, Ammon says that he wants to live with the Lamanites, and the king says, in effect, "Oh, what a good idea. While you are at it, do you want to marry my daughter?" Doesn't something seem rather wrong about this?
In order to give some reason to these circumstances, let us return to the problem as King Lamoni would have seen it. He has the son of the Nephite king of Zarahemla who has voluntarily come among his enemies. So this man, while presented as a captive, is not a captive of war, but has come willingly. Thus there is little political and religious significance in his death or captive-torture. This man has professed that he wants to live among the Lamanites, but it is possible that he could want to do so to be a spy. Thus there is a problem facing the king. He could kill him, but achieve very little, or he could let him live, but worry about what he might do in the future. What the king decides to do is allow him to live, but morally and legally bind him to the Lamanites by marriage. This is no simple marriage, but one into the royal family. Thus the king will allow Ammon to live, but will place him in a position where his social position signifies a change to the Lamanites, and where the king might be able to keep an eye on him.
Ammon counters with a similar proposal, but one without changing his religious, royal, or political allegiance. He asks to be a servant. So what first appears to be silly is really consistent with the text. [Brant Gardner, Book of Mormon Commentary, [http://www.highfiber.com/~nahualli/LDStopics/Alma/] Alma17.htm, pp. 14-15]