So imagine Lyanna married Robert anyway, do you believe Robert would have been able at all to treat Lyanna the way he abused Cersei? In a world where Lyanna marries Robert, Brandon is still alive and it doesn't look like he would suffer anyone mistreating his sister, married or no. And Robert loved Ned as much as he would have Lyanna so wouldn't he risk pissing each Stark brothers off if he ever so much as lay a hand on Lyanna?
So the first thing we have to address here is that Robert is an act first, think later type of guy. In his fits of anger he doesn’t take the time to consider what he’s doing and how he’s hurting people. He just does it. His abuse of Cersei wasn’t a calculated and controlled thing; it came out of his drunkenness or his rage and his inability to accept responsibility for his actions.
Here’s the scene we saw play out in front of Ned:
The queen looked to her husband. “If any man had dared speak to a Targaryen as he has spoken to you-”
“Do you take me for Aerys?” Robert interrupted.
“I took you for a king. Jaime and Tyrion are your own brothers, by all the laws of marriage and the bonds we share. The Starks have driven off the one and seized the other. This man dishonors you with every breath he takes, and yet you stand there meekly, asking if his leg pains him and would he like some wine.”
Robert’s face was dark with anger. “How many times must I tell you to hold your tongue, woman?”
Cersei’s face was a study in contempt. “What a jape the gods have made of us two,” she said. “By all rights, you ought to be in skirts and me in mail.”
Purple with rage, the king lashed out, a vicious backhand blow to the side of the head. She stumbled against the table and fell hard, yet Cersei Lannister did not cry out. Her slender fingers brushed her cheek, where the pale smooth skin was already reddening. On the morrow the bruise would cover half her face. “I shall wear this as a badge of honor,” she announced.
“Wear it in silence, or I’ll honor you again,” Robert vowed. He shouted for a guard. Ser Meryn Trant stepped into the room, tall and somber in his white armor. “The queen is tired. See her to her bedchamber.” The knight helped Cersei to her feet and led her out without a word.
He deals Cersei a vicious blow because he’s drunk and she’s said something he misliked. Cersei recalls a similar altercation in an AFFC chapter:
“I glimpsed him once at Winterfell,” the queen said, “though the Starks did their best to hide him. He looks very like his father.” Her husband’s by-blows had his look as well, though at least Robert had the grace to keep them out of sight. Once, after that sorry business with the cat, he had made some noises about bringing some baseborn daughter of his to court. “Do as you please,” she’d told him, “but you may find that the city is not a healthy place for a growing girl.” The bruise those words had won her had been hard to hide from Jaime, but they heard no more about the bastard girl.
So the record is rather clear that Robert reacts rather violently when his wife says something he doesn’t like or upsets him. I don’t think he actually thinks when he hurts her; he just does. In addition, he does not blame himself. He blames the wine, or he blames Cersei:
For Robert, those nights never happened. Come morning he remembered nothing, or so he would have had her believe. Once, during the first year of their marriage, Cersei had voiced her displeasure the next day. “You hurt me,” she complained. He had the grace to look ashamed. “It was not me, my lady,” he said in a sulky sullen tone, like a child caught stealing apple cakes from the kitchen. “It was the wine. I drink too much wine.” To wash down his admission, he reached for his horn of ale. As he raised it to his mouth, she smashed her own horn in his face, so hard she chipped a tooth. Years later at a feast, she heard him telling a serving wench how he’d cracked the tooth in a mêlée. Well, our marriage was a mêlée, she reflected, so he did not lie.
Robert reached for the flagon and refilled his cup. “You see what she does to me, Ned.” The king seated himself, cradling his wine cup. “My loving wife. The mother of my children.” The rage was gone from him now; in his eyes Ned saw something sad and scared. “I should not have hit her. That was not… that was not kingly.” He stared down at his hands, as if he did not quite know what they were. “I was always strong… no one could stand before me, no one. How do you fight someone if you can’t hit them?” Confused, the king shook his head. “Rhaegar… Rhaegar won, damn him. I killed him, Ned, I drove the spike right through that black armor into his black heart, and he died at my feet. They made up songs about it. Yet somehow he still won. He has Lyanna now, and I have her.” The king drained his cup.
Now, here’s the other thing: Robert had no fear of Jaime of Tywin. Perhaps it was because he was king, but he clearly made no effort to restrain himself so that he wouldn’t be chastened by Jaime or Tywin. According to Cersei, Jaime would have killed Robert if he knew that he hit her:
“If you truly believed that, you would never have come.” Ned touched her cheek gently. “Has he done this before?”
“Once or twice.” She shied away from his hand. “Never on the face before. Jaime would have killed him, even if it meant his own life.”
Cersei hid these bruises from Jaime, perhaps out of fear for his life. After all, if he killed the king, he’d be dead too. So now we can round back around to Lyanna and her brothers.
While a younger Robert might have known more self-restraint, I think it’s safe to assume that these physically abusive behaviors aren’t something that would be cured through a marriage to Lyanna. It’s been discussed before that Robert did not know the real Lyanna. She likely would not have been the soft-spoken, agreeable wife Robert believed she would be, nor would she have loved him the way he wanted her to love him. He might have loved her, or claimed to, but Robert’s love for Lyanna was always an idealistic love. It’s far too easy to say that you love a ghost comprised of all your favorite things about a woman.
So if we assume their marriage sours because Lyanna does not love him and does not meet his standards, then Robert may regress into a drunken piece of shit and similar scenes as the ones outlined above might play out. Would he fear Brandon and Ned? He did not fear Jaime, so I don’t think he’d fear Brandon. Now Ned is a different story. We see above that Ned more or less stares Robert into an admission that he “should not have hit her”. His presence seems to guilt Robert into feeling some form of regret, which drove him into further self-pity about how Rhaegar has Lyanna and Robert has her. Robert clearly loves and respects Ned, and I’d wager that between Brandon and Ned, Robert would be much more affected by Ned’s disappointment than Brandon’s rage.
The thing is, I don’t think Robert would even consider their feelings on the matter until of them approached him with it. Then maybe after a confrontation, Robert may reconsider his actions. But the question to ask is, would Lyanna even tell Brandon or Ned? That’s something that could really go both ways. Lyanna could see telling her brothers as a form of defeat, or in Brandon’s case, fear his reaction or maybe she’d say fuck it, I’m not taking this anymore, and tell one of them. However, assuming they’re both living at Winterfell and share this info with Rickard, I think Rickard would forbid either of them from acting upon their feelings. Lyanna’s duty was to marry him, and I don’t think Rickard really cared what happened within the marriage beyond that.