Hate to hijack this again, but…
My impression of that part of the Illiad was less about loooooove and mostly about Achilles sense of pride as well as Agammenon’s duty as King to make sure loot was justly delivered. It could just as easily have been a really nice sword for all Achilles’ ego would’ve cared. He was the great warrior, so he should get the girl slave instead.
As for the wife and son: and… ? Every greek man, as a matter of course, would’ve had a wife and children. Anything else would be a breach of his masculine duties. On the flipside, a lot of them also had lovers of either gender as a matter of course. The important issue was getting and raising more virtuous sons for your people to use in wars to come. The wife mattered little beyond that and monogamy was a very flexible item. You accorded her a certain amount of respect, you kept things moderately discreet, but those were really the major rules of etiquette.