What do you think was the relationship like between Ned and the different members of the Tully family? Because we are not given much information about it in canon. But did they like him? Certainly less after he brought Jon home right? Sometimes in fanfics they openly hostile towards Ned because of this. But I am not entirely sure if this is accurate. What do you think? 
I don’t think outright hostility really fits the Tullys, at least not as a default, sustained reaction.
They’re a proud family, very conscious of “family, duty, and honor”, but they’re also political and measured. Someone like Hoster knows he wouldn’t gain anything from open aggression toward Ned, who is not only his son-in-law but also Warden of the North. Brynden, for all his bluntness, is still perceptive enough to understand that his restraint matters. He might be more direct, even cutting, but not needlessly cruel. He’s more the type to say exactly what Ned needs to hear and then leave it there.
So instead of open hostility, I imagine disapproval that is clearly expressed, but yk controlled.
I do think they would confront ned about it, though. Butt this is more likely to happen in private conversations in which the gravity what he’s done is made very clear. They would emphasize what bringing Jon home implies: the insult to Catelyn, the potential damage to her standing, and the long-term implications for her trueborn children. They most likely would even suggest that the boy be sent away, but Ned being Ned, he wouldn’t budge. And the Tullys know better than to argue further.
As for Edmure, I actually like the idea that when he’s younger, he might react more emotionally less filtered, more openly upset on Catelyn’s behalf, but he wouldn’t go confronting Ned abt it either. His loyalty to Cat would still be strong, just expressed in a more controlled way.
