In the comics, Homelander doesn't have any offspring. His character is focused more on his own power and struggles rather than having a family with children.
Well, Homelander is a complex and often self - centered character. If he were in an Avengers fanfiction, he might initially see the Avengers as a threat to his own status. He'd probably try to assert his dominance over them, thinking he's superior. He could start by showing off his powers, like his super strength and laser eyes, to intimidate the Avengers. But the Avengers, being used to dealing with powerful foes, would likely see through his bravado and not be easily cowed.