Part 1: Ned Stark does VERY naughty things
Since Ashara Dayne only lives in Robert's Rebellion, I have to go through that particular war. Right off the bat I do two things: One, I decide that I'm going to book it to Starfall, only diverting from my route to avoid excessive attrition and to help win the war. Second, in order to ensure Tywin does not join on the side of Aerys, I marry Benjen off to Cersei. Yes, that Benjen to that Cersei. They actually don't hate each other all that much.
The war takes about a half a year longer than it did canonically, but for the most part it is hilariously one sided. My forces engage in exactly one conflict on my way down to Dorne. My thirty thousand strong army meets an eleven thousand strong army led by Prince Rhaegar, a few counties out from King's Landing. His army is completely massacred and I continue on my way. I assume one of my allies finishes him off later.
After that encounter, there were only three major battles to speak of. All of them were in the Crownlands, and one of them would have turned the tide of the war if the AI had been smart enough to take advantage of it. The first of the three saw the Vale's troops fight their first major battle, against a coalition of smaller, crown loyalist troops. The Vale outnumbered the loyalists by ten thousand men, and handily slaughtered that army.
However, the next battle did not go so well. Robert's seventeen thousand strong army was ambushed by a twenty five thousand strong army led by Randyll Tarly. Robert lost over two thirds of his forces, and Tarly was free to tear shit up in the Crownlands. Unfortunately for the Targaryens, he turned around and marched back into Reach territory. Maybe chasing me, as I was nearing the Prince's Pass, but I don't know. For all intents and purposes, that army disappeared off the map.
The final battle saw the removal of the last significant loyalist army from the Crownlands. Robert took command of his spare army and crushed the seven thousand strong contingent, leaving King's Landing wide open. His forces then set siege to the city, where they would stay for the next few months.
By this time, I had already come down to Starfall and impregnated Ashara Dayne. It took a few reloads to have her stop drinking moon tea (I hadn't yet changed the moon tea requirements) and to bear a son instead of a daughter, but she finally gave birth to a boy, and an attractive one at that. I named him Robb, and through the vagaries of RNG, he was culturally Dornish and of the Faith. (He's older in this picture since I don't have a birth picture for him)
Now this happened in about mid-285 AL, so the War of the Usurper was finished. Aerys the Mad was beheaded, his son Rhaegar sent off to the Night's Watch, and Rhaegar's son Aegon was left with custody of Lyanna, though that didn't remain the case for long.
Shortly after Aerys' defeat, Mace Tyrell decided he didn't like the new order of things and declared Independence. Unfortunately for him, my eighteen thousand troops were still in the area, and I swiftly marched on Highgarden and imprisoned him. His war never gained any traction.
Now here's where the story takes a turn for the strange. You see, I had managed to get Eddard lustful by event, and somehow Lyanna ended back up in my court instead of Robert's. One thing led to another, and I had a Jaime and Cersei couple on my hands. Ladies and gentlemen, meet Lyanna Stark the Brotherfucker:
I knew Ned was a bit of a hard ass, but I didn't really picture him as being incestuous. In any case, Jaime and Cersei 2.0 had an affair, and in true LanniStark style, they pulled a Joffrey. Or. in other words, a pureblood Stark was passed off as a Baratheon.
While Eddard Stark lay in bed with his sister, he suddenly remembered about Cersei. Being the lustful man he was, he tried to get into her pants. She refused, but Eddard Stark wouldn't be denied. He gave her an offer: he puts her on the Lord Paramountcy of the Westerlands, and she lets Eddard fuck her. She agrees.
Now, the Westerlands are more powerful than the North at this point in time. In order to win, I need more troops... I know! Edmure Tully! He's currently allied with me, and a little gold butters him up to kick some Lannister butt. Funny side note: In this time, Tyrion Lannister is a Formidable Fighter. Yes, you read that right. Tyrion Lannister is considered on par with Ser Arthur Dayne by ranking. Still, his swordplay doesn't save him from fifty thousand Stark and Tully troops, and after being led into a trap on the Gold Road, capitulates to Eddard Stark and his sister. Cersei gets Casterly Rock, and Eddard gets to fulfill his twisted desires.
Now it's around this time that Robb Sand comes of age. Thinking that a North/Dorne alliance would be both impractical and yet hilarious, I marry Robb Sand to Princess Arianne, give him Ice because he's a much better soldier than my legitimate son, and give him the cadet dynasty of Blackstark and Flint Keep. I then switch to play as him, since that was the entire point of this exercise.
When I switch, I see Arianne has a daughter from her previous marriage that I violently terminated, and a son from Robb. The boy is attractive, like his parents, and is named Jon. I quickly arrange for the death of my stepdaughter to ensure that Dorne goes to the Starks and not the Martells.
Now, those of you aware of how the cadet dynasty decision works know that I should not be a bastard, and you would be correct. However, since I am ahead of my brother in the line of succession should I be legitimized, I edited the save game to reset legitimized bastard to normal bastard. Gotta work for the North.
A few years prior to my switch, Robert died in a suspicious accident. I don't know who killed him. What I do know is that a few years prior to his death, he found out about the affair and demanded it to be ended. Being the honorable guy Eddard Stark was, he refused on the spot. Eddard and Lyanna then went and had rage-sex which resulted in a stillborn Stark. Maybe Lyanna was behind his death. In any case, what happens is that Mina Starkratheon takes the throne, and pretty quickly things turn to shit. Cersei Lannister decides she really doesn't want Casterly Rock, and declares a tyranny war on little Mina Baratheon. Unfortunately for her, Eddard Stark is on the case, and very quickly Cersei is defeated. She is stripped of the Westerlands and then released at the behest of Eddard Stark.
Eddard Stark then decides to secure his house's position as the most influential one in Westeros, and marries off his first two trueborn children. The eldest, the daughter, is betrothed to the under age Lord Paramount of the Vale. The younger son, Rickard, is betrothed to his half-sister Mina Baratheon, Queen of the Iron Throne. Ned Stark really likes to keep it in the family, eh?
However, Mina Baratheon is attacked by the Lord Paramount of the Stormlands for some reason, and Eddard Stark goes off to defend the honor of his daughter. He does not return.
Thus ends the life of Eddard Stark the Sisterfucker, going to his grave without understanding what monogamy was. He left behind nine kids, four from Catelyn Tully, three from Ashara Dayne, and two from Lyanna Stark. Unfortunately, the last two kids of Ashara Dayne and Lyanna Stark's second child were all stillborn, leaving Eddard Stark with only six living children, of which only five were publicly acknowledged to be his. A rather good start, wouldn't you say? Oh, and Cersei manages to regain her position as Lady Paramount of the Westerlands, probably via faction.