Even on the chapter where Viserys finally dies, Daenerys continues to be submissive to her older brother until a specific event, which I'll further discuss later. This poor girl is raised only by her abusive brother and is taught that she owes him obedience and loyality because he's the true king and her only relative. What is more, for years he has threaten her that if she disobeys him, she'll "wake the dragon" in him. And by waking the dragon he means that he'll abusive her both emotionally and physically (sometimes even sexually). Viserys has no shame to use abuse towards his little sister when he's in a fool mood and he always let her know that it's her own fault ( as many abusers do with their victims).
Look how Dany reacts when she finds out that Viserys tried to stole her eggs:
For a moment Dany was so shocked she had no words. "My eggs … but they're mine, Magister Illyrio gave them to me, a bride gift, why would Viserys want … they're only stones …"
"The same could be said of rubies and diamonds and fire opals, Princess … and dragon's eggs are rarer by far. Those traders he's been drinking with would sell their own manhoods for even one of those stones, and with all three Viserys could buy as many sellswords as he might need."
Dany had not known, had not even suspected. "Then … he should have them. He does not need to steal them. He had only to ask. He is my brother … and my true king."
She's willing to give away her eggs to her brother if he asks her to. She even try to justify it by saying that he's her brother and her king. This isn't Dany giving away a pretty present she got, she's willing to give away those eggs which brought her comfort when she was at her lowest when she first joined the Dothraki. It shows that there is almost nothing that Dany wouldn't give to Viserys if he asked her no matter how dear it was to her.
Continuing her conversation with Ser Jorah she explains that Viserys is all the family she has left:
"He is your brother," Ser Jorah acknowledged.
"You do not understand, ser," she said. "My mother died giving me birth, and my father and my brother Rhaegar even before that. I would never have known so much as their names if Viserys had not been there to tell me. He was the only one left. The only one. He is all I have."
Poor Dany, for thirteen years she only family she got was an older brother who often abused her.
When Viserys enters Vaes Dothrak and draws his sword - something that is forbidden within the city according to Dothraki laws- Dany tries to make him see reason and even offers him her eggs which she believes that could calm him down. This time she's terrified both of and for him.
"The blade … you must not," she begged him. "Please, Viserys. It is forbidden. Put down the sword and come share my cushions. There's drink, food … is it the dragon's eggs you want? You can have them, only throw away the sword."
However, the moment Viserys threatens her belly with his sword, the narrative stops refering to him as Daenerys' brother. That's because he's no longer threatening only Dany but her unborn baby as well. Her mother instict kicks in and she won't allow Viserys to abuse her child like he did with her. The moment he puts her unborn son in harm while he's threatening her, Viserys crosses the line and there is no turning back. He's no longer her brother or her king daand she feels neither obendiance nor loyalty towards him.
The sword point pushed through her silks and pricked at her navel. Viserys was weeping, she saw; weeping and laughing, both at the same time, this man who had once been her brother.
Viserys keeps being referred as "the man who had been her brother" until his death.
"What did he say?" the man who had been her brother asked her, flinching.
When the sun of her life reached her, Dany slid an arm around his waist. The khal said a word, and his bloodriders leapt forward. Qotho seized the man who had been her brother by the arms
At the last, Viserys looked at her. "Sister, please … Dany, tell them … make them … sweet sister …"
When the gold was half-melted and starting to run, Drogo reached into the flames, snatched out the pot. "Crown!" he roared. "Here. A crown for Cart King!" And upended the pot over the head of the man who had been her brother
Daenerys' brother and abuser is finally dead. She has the epiphany that he's not a real dragon. Viserys had her convinced that he was the real dragon, someone who inspired fear on her. But on the last few months, she started having dragon dreams and she has already connected with her dragon eggs. She has seen a different side of the dragon, not being embodied by someone she fears but the dragon(s) as a source of comfort, feeling as home. Between the dragon as a source of fear and the dragon as a source of familiarity and comfort she chooses the second and therefore Viserys no longer fits on her perspective of what makes someone a dragon. He's not a dragon, he's a pathetic man who threatened his pregnant sister he had sold to slavery.