Unpopular opinion but Goldanna doesn't deserve as much hate as she gets.
As far as she's aware, her mother was raped by King Maric and then died in childbirth. And before she even gets to really process her grief, she's sent away with a single sovereign in hand and nothing else. She tries to come back to the castle when her money's run out and she needs work, and they chase her off because they can't have her spreading rumours about Maric's bastard. Especially not when they really do have Maric's bastard in the castle, and they've been telling him that his mother was a maid. (Seriously what are the odds that Eamon took advantage of that one maid that everyone knew had been pregnant and died, and figured that she would be a good cover story for Alistair?)
Anyways Goldanna gets to Denerim and sets up a life for herself. She spends her days washing linens and rearing her children, working hard to keep them fed, when who walks in the door? A bunch of strangers, one of whom claims to be her brother. The brother that (as far as she knows) robbed her of her mother.
Goldanna is a character wrapped up in bitterness and unresolved trauma for Good Reason. Does Alistair deserve her taking it out on him? Of course not. He'd just wanted to connect with whatever family he could find and be a part of that family, but Goldanna suffered greatly as a result of what happened to her mother and the consequences that her death had for her. It screams of being an old wound that never really healed, and she's bitter for how she was treated in the wake of it. Alistair was unfortunate in that he was the most tangible target that Goldanna's had for her frustrations since leaving Redcliffe, especially since we've since learned that he was never Goldanna's brother to begin with. But he doesn't know that, and neither does Goldanna.
So no, he didn't deserve to be spoken to that way, but what bothers me is that where that quest ends and we're left only with the take away that everyone out for themselves and that Goldanna was the only one in the wrong when the reality is that the fault lies with the person responsible for their situation: Arl Eamon.
In fact, Alistair's personal quest would have been a brilliant opportunity for him to reflect upon and challenge his views of Eamon as this faultless, honourable man who always goes the right thing, when just hearing anything about how Eamon 'raised' Alistair made it pretty clear that he was a terrible guardian.
Alistair always views the way he was treated as 'understandable' because he's Maric's bastard, Isolde was insecure over the rumours, Eamon was doing what was best for Alistair and Ferelden and blah blah blah. All excuses, and Alistair accepted all of them. But finding out that Eamon had a grieving young girl thrown out onto the streets right after losing her mother, it would make sense for him to pause and think 'why would the arl ever do that? He looked after me, why not look after my sister too?' and then actually challenge his belief that Eamon is unassailably good and honourable. Maybe the Warden could even encourage him to confront Eamon about what happened to Goldanna or leave it be, which results in Hardened Alistair vs Unhardened Alistair, and a confrontation could result in Eamon agreeing to send reparations to Goldanna (if only to placate Alistair), as opposed to forcing Alistair to give her money or nothing at all. Actually making the person who should have been held accountable for Goldanna's situation... well, accountable.
Tldr; Alistair's personal quest could have had him challenging his belief that Arl Eamon is a good, honourable man without faults and learning to stand up to him, rather than painting a poor, working class woman as a horrible monster because she's bitter and mean about *checks notes* the rape and death of her mother.
