I offer three separate quotes from our author regarding marriage and his thoughts about how he presented them realistically with regard to the time period:
“And then there are some things that just don’t square with history. In some sense I’m trying to respond to that. [For example] the arranged marriage, which you see constantly in the historical fiction and television show, almost always when there’s an arranged marriage, the girl doesn’t want it and rejects it and she runs off with the stable boy instead. This never fucking happened. It just didn’t. There were thousands, tens of thousands, perhaps hundreds of thousands of arranged marriages in the nobility through the thousand years of Middle Ages and people went through with them. That’s how you did it. It wasn’t questioned. Yeah, occasionally you would want someone else, but you wouldn’t run off with the stable boy.........”
“And that’s another of my pet peeves about fantasies. The bad authors adopt the class structures of the middle Ages <snip> they have scenes where the spunky peasant girl tells off the pretty prince. The pretty prince would have raped the spunky peasant girl. He would have put her in the stocks and then had garbage thrown at her. You know. I mean, the class structures in places like this had teeth. They had consequences. And people were brought up from their childhood to know their place and to know that duties of their class and the privileges of their class. It was always a source of friction when someone got outside of that thing. And I tried to reflect that (GRRM).”
“Marriage was a form of political alliance. It was a way to cement a political alliance – one of the ways to bind two families together and hopefully make peace between them or to establish that... they would be allies against a third common enemy. You didn’t want your sons or daughters, if you were a lord, marrying for love. That was, that was insane... If you had a vassal whose loyalty you questioned, maybe you married him to one of your daughters and thereby bind him more closely to the family. If you have a rival you’d been at war with and now you make peace, you marry a daughter to his son...”
That last sentence about making peace by marrying your daughter to his son is exactly what Tywin did. He made an alliance with Robert through a marriage pact with Cersei. I propose that this agreement happened much, much earlier than we have been led to believe.
Ned knew something dishonorable had taken place and he tried to tell Robert about it, but Robert already knew:
“Seven hells, someone had to kill Aerys!” Robert said, reining his mount to a sudden halt beside an ancient barrow. “If Jaime hadn’t done it, it would have been left for you or me.”
“You took a wound from Rhaegar,” Ned reminded him. “So when the Targaryen host broke and ran, you gave the pursuit into my hands. The remnants of Rhaegar’s army fled back to King’s Landing. We followed. Aerys was in the Red Keep with several thousand loyalists. I expected to find the gates closed to us.”
Robert gave an impatient shake of his head. “Instead you found that our men had already taken the city. What of it?”
“Not our men,” Ned said patiently. “Lannister men. The lion of Lannister flew over the ramparts, not the crowned stag. And they had taken the city by treachery.”
The war had raged for close to a year. Lords great and small had flocked to Robert’s banners; others had remained loyal to Targaryen. The mighty Lannisters of Casterly Rock, the Wardens of the West, had remained aloof from the struggle, ignoring calls to arms from both rebels and royalists. Aerys Targaryen must have thought that his gods had answered his prayers when Lord Tywin Lannister appeared before the gates of King’s Landing with an army twelve thousand strong, professing loyalty. So the mad king had ordered his last mad act. He had opened his city to the lions at the gate.
“Treachery was a coin the Targaryens knew well,” Robert said. The anger was building in him again. “Lannister paid them back in kind. It was no less than they deserved. I shall not trouble my sleep over it.”
“You were not there,” Ned said, bitterness in his voice. Troubled sleep was no stranger to him. He had lived his lies for fourteen years, yet they still haunted him at night. “There was no honor in that conquest.”
“The Others take your honor!” Robert swore. “What did any Targaryen ever know of honor? Go down into your crypt and ask Lyanna about the dragon’s honor!”
“You avenged Lyanna at the Trident,” Ned said, halting beside the king. Promise me, Ned, she had whispered.
“That did not bring her back.” Robert looked away, off into the grey distance. “The gods be damned. It was a hollow victory they gave me. A crown … it was the girl I prayed them for. Your sister, safe … and mine again, as she was meant to be. I ask you, Ned, what good is it to wear a crown? The gods mock the prayers of kings and cowherds alike.”
“I cannot answer Grace … only for what I found when I rode into the throne room that day,” Ned said. “Aerys was dead on the floor, drowned in his own blood. His dragon skulls stared down from the walls. Lannister’s men were everywhere. Jaime wore the white cloak of the Kingsguard over his golden armor. I can see him still. Even his sword was gilded. He was seated on the Iron Throne, high above his knights, wearing a helm fashioned in the shape of a lion’s head. How he glittered!”
“This is well known,” the king complained.
“I was still mounted. I rode the length of the hall in silence, between the long rows of dragon skulls. It felt as though they were watching me, somehow. I stopped in front of the throne, looking up at him. His golden sword was across his legs, its edge red with a king’s blood. My men were filling the room behind me. Lannister’s men drew back. I never said a word. I looked at him seated there on the throne, and I waited. At last Jaime laughed and got up. He took off his helm, and he said to me, ‘Have no fear, Stark. I was only keeping it warm for our friend Robert. It’s not a very comfortable seat, I’m afraid.’”
“Well, now I know Jaime’s dark sin, and the matter can be forgotten. I am heartily sick of secrets and squabbles and matters of state, Ned. It’s all as tedious as counting coppers. Come, let’s ride, you used to know how. I want to feel the wind in my hair again.”
You can read the above two ways. You can view this through Ned's eyes and his belief that Robert wasn't aware of the Lannister's treachery and his belief that they wanted the throne for themselves, or you can read between the lines and realize that Robert knew everything all along because he was a willing participant in the treachery. He calls the Lannisters that sacked Kings Landing "our men"...Ned says "not our men", but Robert called them "our men", because the Lannisters were already his ally.
Lyanna was already dead by the time Robert and Ned reached the Trident. That he "avenged" her there indicates that they both knew she was dead, and Robert's words that his vengeance "did not bring her back" also supports this.