None of the answers actually deal with Daenerys's fond memories of Viserys which is understandable because most of that information was not released when this question was asked or answered (A Dance With Dragons only came out in July 2011).
Relationship of Viserys and Daenerys
Viserys bore a great burden on his shoulders since his father died. He was no more than a child of 8 and he had the responsibility to restore an almost three hundred years old dynasty to its rightful place. The task is even more huge if you consider the Valyrian noble background of Targaryens which goes back to at least 5,000 years. To make matters even worse, he was born out of incest of parents who themselves were born out of centuries of incest. He inherited the notorious Targaryen madness unlike his siblings.
After his death, Daenerys misses him. From ASOS Chapter VIII:
Viserys had been stupid and vicious, she had come to realize, yet
sometimes she missed him all the same. Not the cruel weak man he had
become by the end, but the brother who had sometimes let her creep
into his bed, the boy who told her tales of the Seven Kingdoms, and
talked of how much better their lives would be once he claimed his
This shows that before Viserys went insane, he was kind to her.
As children, without a doubt Viserys showed kindness to Dany as any elder brother would have done. But years of mockery and failures made him a bitter man who could channel his anger on no one except the little sister he had protected until then.
When they hit the bottom and became completely pennyless, Viserys, though getting sicker and sicker, used to reassure her:
“We will have it all back someday, sweet sister,” he would promise
her. Sometimes his hands shook when he talked about it. “The jewels
and the silks, Dragonstone and King’s Landing, the Iron Throne and the
Seven Kingdoms, all they have taken from us, we will have it back.”
We can establish that destruction of their relationship began after Viserys was forced to sell Queen Rhaella's crown in order to avoid starvation.
From ASOS Chapter 27:
When Viserys sold their mother's crown, the last joy had gone from him
Daenerys did not help either. As Daenerys was his heir, naturally he would have expected greater ambition from her in order to do things that needed to done. While on a voyage, Daenerys talked about how amazing it would be to be a sailor. While that was of course an innocent childish comment, It must have felt like a whip to him. He screamed at her that she was blood of the dragon, not some smelly fish.
Daenerys eventually came to understand why he became what he was. From ACOK chapter 40:
I have become the most splendid beggar in the world, but a beggar all
the same. She hated it, as her brother must have. All those years
of running from city to city one step ahead of the Usurper's knives,
pleading for help from archons and princes and magisters, buying our
food with flattery. He must have known how they mocked him. Small
wonder he turned so angry and bitter. In the end it had driven him
mad. It will do the same to me if I let it.
Later Daenerys has another hallucination about him which was basically her own subconscious chiding her. From ADWD Chapter 71:
"You are dead,” Dany said.
Murdered. Though his lips never moved, somehow she could hear his
voice, whispering in her ear. You never mourned me, sister. It is hard
to die unmourned.
“I loved you once.”
Once, he said, so bitterly it made her shudder. You were supposed to
be my wife, to bear me children with silver hair and purple eyes, to
keep the blood of the dragon pure. I took care of you. I taught you
who you were. I fed you. I sold our mother’s crown to keep you fed.
“You hurt me. You frightened me.”
Only when you woke the dragon. I loved you.
“You sold me. You betrayed me.”
No. You were the betrayer. You turned against me, against your own
“You could have had your crown,” Dany told him. “My sun-and-stars
would have won it for you if only you had waited.”
I did wait. For my crown, for my throne, for you. All those years,
and all I ever got was a pot of molten gold.
Daenerys had always been a shy, timid girl who obviously loved her brother before he went mad. She remained the shy timid girl until Drogo's love gave her confidence and all the weakness was burned from her at Drogo's pyre. That timid girl did what her brother wanted because he was her King and she wanted to see Three headed dragon flying atop the Red Keep once again, just as much as Viserys did. She was also scared of Viserys and his moods. Which is why she did what she was told but not before getting scared and begging Viserys to let her go back.
This man frightened her. “I don’t want to be his queen,” she heard
herself say in a small, thin voice. “Please, please, Viserys, I don’t
want to, I want to go home.”
Daenerys did not hate the Dothraki as you assume. She considered them Barbarians and was afraid of their violent reputation.
Yet, he was the only family she had. She explained it to Ser Jorah in AGOT Chapter 46:
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
She did consider him her true King until Ser Jorah convinced her otherwise after he attempted to steal her dragon eggs:
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.”
Not to mention she came to fear Viserys when she was in his power as he used to hurt her after he lost all sanity. From AGOT, in Dany's own thoughts:
She knew better than to question her brother when he wove his webs of
dream. His anger was a terrible thing when roused. Viserys called it
“waking the dragon.”
And also the event when Viserys brought Dany a dress. From AGOT:
"You don’t want to wake the dragon, do you?” His fingers twisted her,
the pinch cruelly hard through the rough fabric of her tunic.
“Do you?” he repeated.
“No,” Dany said meekly.
Viserys did what he could to feed and protect Daenerys until he went mad. Without him to teach her what she was, she would have probably ended in some Lysene pillowhouse or would have been forced to become a Courtesan in Braavos when their servants took over their house after death of Ser Willem (the man who ferried them out of Dragonstone to escape Robert's iron clutches).
As evident from Dany's thoughts, he was not always the weak and cruel man as we see him in first book/first episode. He was her brother once, the brother she loved and the brother who loved her back. But sadly he was mad which is not really his own fault. In his own mad way, he started to resent her for death of their mother, for Robert's rebellion and for everything. She became the cause of everything wrong that happened to him in his mind. No doubt he hated himself for becoming the Beggar King which only accelerated his descent into the realm of madness.