Superman isn't the star on Supergirl's show and him talking a back seat is fine. There's more to him than punching bad guys. Except super-heroes having kids is not the norm, especially not live action Superman. The only time this happened in the past was Superman Returns, and Superman was a dead beat dad in that. Characters evolve, which Superman does over time so him having kids is a more mature Superman rather than staying in the same old routine. They clearly have ideas since they're making a show about Superman with these kids.
They're been improving in tv and movies the last few years, the problem is that Snyder's kneecapped Cavill so they can't rely on him as much as they used to. Wonder Woman's had bigger issues with DC management, yet she's got a movie sequel coming out by Patty Jenkins.But it's as you seem to note in this post, I don't think it's that they hate superman. It's just that they don't know what to do with pretty much all DC comics character besides the Bat family so they place all their chips on him.