Achilles and Hector both have entirely different relationships with their fellow countrymen than the other. Hector’s relationships tend to have a smooth unity to them thought the story. He only seems to ever face conflict from either fellow soldiers calling him back to battle or his own family wishing him to stop fighting. This allows the relationships that Hector has to be one of the his major sources of strength in the story and one of his main drives to fight.
In contrast Achilles’s relationships with his fellow Achaeans seem to be a hodgepodge of close friends and hated allies. With a large part of the relationship that Achilles has with these people seeming highly dependent upon how Achilles status is perceived. Causing Achilles to take actions that force the Achaeans to continue to rely on him like asking his mother to talk to Zeus about flipping the direction of the war. Which shows that the dependence of the relationship is felt on both sides.
Hector and Achilles seem to have a very indirect relationship. They both rarely seem to mention one another beyond a few passing lines but both regard the other as a significant part of the war. Achilles seeing Hector as the only challenge that the war may offer him. While Hector sees Achilles as a force of nature that will crush him that he must still find an answer to.
After Achilles enters his berserker episode he is brought back to balance by Priam. Priam does this by risking his life and entering the Achaeans camp with the guidance of Hermes. Achilles is so surprised and impressed by this that when he first sees Priam he asks Priam if he is a god. The courage and love for his son that Priam shows when he does this reminds Achilles of his father and Patroclus and units them in grief. With Achilles transformation communicating that you have to move beyond grief and go on with life. As soon as Achilles realizes this he passes this on to Priam with the story that he tells him about Niobe and her children. Showing that even though the gods killed all of her children Niobe exhausted from grief had to continue to eat. This little tale signifying that even when grief cripples you you must remember to live on.
Sadly the Warrior code and the Familial code, at least when it comes to the greeks, is not mutually exclusive. This is because to have a family you have to at the very least be able to prevent your family from being taken from you. That means that in those times you had to be able to fight and fight well which is where the code of the Warrior came in. Its easy to see this play out with the talk Hector has with his wife Andromache about the worry he faced when the greeks would enslave her. Which to prevent demanded his attention as a warrior for if he did not fight for his family who would.