Here I go again... maybe this deserves his own post. Ok, I actually make it
I appreciate your efforts, and even mentioning me (upvote) but I don't buy it. I will like to apply Occarn's Razor: The simplest possibility is the more likely possiblity, or something like that.
Before anything, Ashara is one of the biggest mysteries of the series. We know little of her and can only speculate.
[This are all mentions of Ashara in the series]http://asearchoficeandfire.com/?q=ashara&scope[]=agot&scope[]=adwd&scope[]=twoiaf&scope[]=acok&scope[]=thk&scope[]=trp&scope[]=asos&scope[]=tss&scope[]=tpatq&scope[]=affc&scope[]=tmk)
The passage from the tale of the Knight of the Laughing Tree
And this interesting So Spoke Martin
In the wiki it says that her body was never recovered, but I haven't found any reference to it in the Arya chapter, althought it is a logical conclusion if she throw herself into the sea. It also says that she committed suicide shortly after the end of Robert's Rebellion, again without references. So, we don't know when she commited suicide, or if she even did.
Okay, the mayor point regarding this thread. The stillborn daughter. That and the suicide are only known by rumors, so it is not reliable.
Ser Barristan is the only POV that mentions Ashara had a stillborn. He even tells us that the stillborn was a daughter. But he has only heard rumours. How could he know even his gender?
He says this after thinking of Daenerys' eyes and how she looked like Ashara's daughter.
So, maybe this is an assumption made by Barristan after thinking of the similarity of Daenerys with Ashara and having heard rumours that she killed herself after losing a child. But...
Cercei in Eddard XII says that he stole a child from Ashara, refering to Jon Snow. So, she thinks that Neds fathered Jon Snow from Ashara Dayne, like Catelyn does.
Harwin, in the Arya chapter doesn't mention any child
Was ever Ashara Dayne even pregnant? Did she really commit suicide? We don't know, we can't make assumptions based on this as if it were a fact
All romours and text evidence points out that the man who dishonored her at harrenhal was Eddard Stark.
Yes, "might she have looked to me instead of Stark?" is ambiguous, doesn't specifically mentions Ned and doesn't necessarily means that they have sex at all. I'll give you that. You can come with all the tinfoil you want here.
-A Storm of Swords, Arya VIII
"My father was Ser Arthur's elder brother. Lady Ashara was my aunt. I never knew her, though. She threw herself into the sea from atop the Palestone Sword before I was born."
"Why would she do that?" said Arya, startled.
Ned looked wary. Maybe he was afraid that she was going to throw something at him. "Your lord father never spoke of her?" he said. "The Lady Ashara Dayne, of Starfall?"
"No. Did he know her?"
"Before Robert was king. She met your father and his brothers at Harrenhal, during the year of the false spring."
"Oh." Arya did not know what else to say. "Why did she jump in the sea, though?"
"Her heart was broken."
Sansa would have sighed and shed a tear for true love, but Arya just thought it was stupid. She couldn't say that to Ned, though, not about his own aunt. "Did someone break it?"
He hesitated. "Perhaps it's not my place . . ."
"Tell me."
He looked at her uncomfortably. "My aunt Allyria says Lady Ashara and your father fell in love at Harrenhal—"
After that, talking with Harwyn:
"I'm not afraid," she said. "That boy Ned said . . ."
"Aye, he told me. Lady Ashara Dayne. It's an old tale, that one. I heard it once at Winterfell, when I was no older than you are now." He took hold of her bridle firmly and turned her horse around. "I doubt there's any truth to it. But if there is, what of it? When Ned met this Dornish lady, his brother Brandon was still alive, and it was him betrothed to Lady Catelyn, so there's no stain on your father's honor. There's nought like a tourney to make the blood run hot, so maybe some words were whispered in a tent of a night, who can say? Words or kisses, maybe more, but where's the harm in that? Spring had come, or so they thought, and neither one of them was pledged."
(Now I'm going to sleep, its late, tomorrow I'll be able to discuss)