Goldanna was a bitter shrew. The idea of them being related was baseless. She doesn't take the chance to know anything about him before trying to manipulate him into giving her money, and even if you do give her money she kicks the Warden and Alistair out. Her life may have been bad, but she can't put the blame on a man she just met. It isn't like Alistair's life was a walk in the park. Being disowned by his father and lied to about his mother's fate. Only to be handed over to Arl Eamon who then sent to the Chantry where he was unhappy, because the Arlessa grew suspicious and jealous.
edit: actually.. that does sound a lot better than Goldanna had it, but it matters not! She was still horrible.
I once read a decent fanfic about Goldanna that helped me understand her better. Imagine you were someone who's mother died when you were too young to take care of yourself. You're given 'hush money' for whatever reason (you are told it's because she gave birth to a child of the king--who killed her). The one person in your world who loved you and you could count on was dead.
Eamon never saw to her care, she was turned out into the streets to fend for herself. His first duty to his peasants would have been to take care of the widows and orphans but she was abandoned. The only skill she had was washing clothes, a sorry thankless job with long hours. She probably turned a few extra coins with 'washing perks' which kept food in her mouth and a sorry shack over her head and gave her a half dozen extra mouths to feed.
Now the child who killed her mother comes into her sorry home. He's not only a prince, but grew up in Eamon's castle, a grey warden and he's well off from the look of him. Clean, healthy, fine armor and weapons in his possession. Definitely with more money than she's probably seen her entire life. She doesn't want to hear about how he had it 'so bad' with not only a roof over his head, food in his mouth, clothes on his back but an education that ensured he wouldn't have to do grunt work all his life to feed himself and his family. Or worry about where his next meal was coming from.
As bad as we know the particulars were for Alistair, he could have had it much worse were he not the son of a king. And from Goldanna's perspective, he had it pretty damn good.
The only time she loosens up on her "I hate you" tirade is if you are a male warden. You depart her home, not on a high note but a promising one between her and Alistair because you can actually get her to listen to him.
Yes, she's a shrew and I dislike her, but I also feel very, very sorry for her. And in light of the recent retcon on Alistair's birth this is even more so because it was so unnecessary to do all that to a child.