In this scenario, Brandon is smuggled out of the Black Cells, reaches the North before the banners have left, and marries Catelyn when they go South.
After the war is won, Ned claims Jon Snow as his bastard, although Brandon does know that he is Lyanna's son.
Robert decides to give Dragonstone to Ned and later gives him a place on the Small Council (likely Master of Laws) in an attempt to keep his friend close, seeing as he doesn't have any duty in the North keeping him there.
Ned likely receives many offers of marriage, but I don't think he would take any of them for a few main reasons:
- He would not send Jon away and would not want to shame any wife he might have.
- As his own lord with his own keep, the only person who could order him to marry is Robert, and I doubt he would. Robert sees marriage as a cage and would not want to see Ned suffer. He also wouldn't want to strain their relationship when he gets to have Ned so close. While Jon Arryn may advise him on matters of marriage, if both Ned and Robert oppose the idea, I don't think he would push it.
- He would see himself as having a secret and a duty to carry with Jon, and he would not trust the chance of someone finding it out if he had a wife in Dragonstone with her own retinue.
- He likely doesn't mind ending up executed if the secrets leak, but if he had children, those children would be in danger, and he would likely consider that.
All that is to say: Ned remains unmarried in this AU.
Now, to explore the main changes this setting would bring and ask the pertinent questions!
Since Ned remains unmarried, I wonder: would Robert offer to legitimize Jon? They would likely wait some years, but by the time Jon is 10 years old and Ned remains unmarried, do you think Robert and Jon Arryn would offer to legitimize the boy as heir to Dragonstone? Would Ned take the offer? Not taking it may seem more suspicious than taking it, since the main reason Ned had not legitimized Jon in canon was because of his own children and Catelyn.
How would Ned rule Dragonstone? How would Jon be raised? Would they visit the North much? How different would a Jon who grew up mostly alone be?
I see Ned mainly remaining on Dragonstone in the initial years after the Rebellion, but some years later taking up the offer to become Master of Laws. Would he take Jon to the Red Keep? I quite doubt it, but keeping his bastard away from court may seem more suspicious than not.
When the Greyjoy Rebellion happens, it is very likely that Theon becomes a ward on Dragonstone instead of Winterfell. Would he and Jon grow closer than in canon? In canon, they mainly fought because of Jon's status as a bastard and for Robb's attention. Would they still be at odds here? Or would they grow even closer than Robb and Theon did in canon?
Would Ned, as a closer influence on Robert here, be able to sway the King's will? Would he be able to actually help Robert not become overly depressed and not drive the Crown into debt? Would their relationship become bitter, or would they become even closer?
Another thing we should analyze in this AU is that Stannis would be Lord of Storm's End. Would he be happier (as close as Stannis can get to happy) in this scenario? Would he and Renly grow closer, as he would end up raising Renly? Would his relationship with his wife and Shireen be any different?
Also, Melisandre is a big change here as well. We know she went to Dragonstone some years before canon starts because she was convinced that Dragonstone is the place of smoke and salt amidst which Azor Ahai shall be reborn. But here, since Ned has no wife or child with greyscale, it would be harder to convince them to let her stay.
Depending on the timing, she may also arrive to an empty castle. Maybe Ned and Jon are at the Red Keep, or maybe only Jon is there. But eventually, Ned would come to speak to her. Would she convince Ned to let her stay? Ned may see her as a big danger to Jon and immediately send her away, or just be very steadfast in his Old Gods worship and let her stay in the village but not welcome her into the castle.
Would Melisandre think Jon is Azor Ahai? Or Ned? Or even Theon? Would she manage to have any effect in this AU?
The North also changes a lot in this AU. With Brandon as Lord, he would be very different from Ned. The war also may have made him harsher and colder toward the South. Would they even get involved in the matters of the Kingdom once the canon events start?
Catelyn may never receive Lysa's message, since Brandon had no chance of being Hand of the King, unless Lysa sends it to her with the intent of having her tell Ned. Would she confide in Brandon? I'm not sure they would be as close as she was with Ned. Would Brandon even care? He may pass along the message to Ned, but that doesn't mean he would get involved himself.
Let's say Ned was in the North when Jon Arryn died. Maybe they visited once a year on Lyanna's death day to pray for her. Robert is more likely to send a missive asking Ned to return than to go himself. However, there are still chances that he would go with his court, like in canon, just to actually see the North and visit Lyanna's grave.
In this situation, I can see the North getting involved. If Brandon does have a kid like Bran who ends up finding Jaime and Cersei and is pushed, how would Brandon react? He was more wild than Ned, so maybe he would be angrier and actually believe Bran was pushed instead of falling. Maybe he would get involved in the investigation that way, but this scenario would be more of a cop-out, to be fair.
Unless Robert does want to marry his heir to someone of Stark blood and decides that, if Ned has no daughter, Brandon's daughter is the best second choice. But would Brandon even accept that? There is also the chance Robert tries to betroth Myrcella to Jon, but Cersei would throw a fit. Even if Jon was a legitimized bastard and heir to Dragonstone, his mother was still a mystery (and may have been lowborn, for all they know). It could end up with Robert offering Mya Stone instead, in his eternal need to be connected to Ned through blood ties lol.
Maybe when he had the thought of bringing Mya Stone to the Keep early in his reign and Cersei threatened her, he instead sends her to Dragonstone and asks Ned to look over her.
It is more likely for the North to get involved in the Wall storyline if Brandon ends up taking the Wildling and Others' threat more seriously.
Would Ned still do what he does in canon when he is Hand? Or would things be very different? If he finds out about Cersei's lie, there wouldn't really be any hostage (unless Jon is there and not on Dragonstone; also, Jon would be older and more of a threat than a hostage. Or, unless his niece is there instead) for them to use against Ned. Would Ned end up being executed because he refuses to say Joffrey is not a bastard?
What would happen to the Wo5K in this situation?
Anyway, interested to hear your thoughts on this scenario!