IS leader Abu Bakr al-Baghdadi also made the 22-year-old his fourth wife, while threatening her with death if she didn't convert to Islam, the Yazidis have told the BBC.
Dalal, who was 15 when she was captured by Islamic State and taken to a slave market, claims she was forced to share a cell with Kayla Mueller after she and a younger girl, Susan, who was 13, were caught trying to escape from IS leader Baghdadi's house.
Dalal said Kayla was taken from the cell one evening and returned the next day, telling the girls: "He made me his wife and he raped me".
"She did everything Baghdadi wanted. She was too afraid to beg.
"When she came back [from seeing Baghdadi], sometimes she just lay down without saying a word. Sometime she would cry under a blanket. She tried to hide that from us. She didn't want to upset us. She wanted to seem strong," said Susan.
The Yazidi girls say they asked Kayla to run away despite Baghdadi's threats about what would happen but she refused.
"No, they will behead me like my journalist friends," she said.
"She was very afraid about getting beheaded," said Dalal. "But she was also very careful about us."
The Yazidi girls have said Mueller, who was kidnapped in Syria in August 2013, tried to look after them: "When IS brought food for us, Kayla ate very little. She didn't want us to be hungry.
"Kayla was like a sister or a mother to us. When we cried, Susan and I, she would tell us: 'You will get home. You will see your parents again.' She was very kind person. I will never forget what she did for us."
According to IS, Kayla was killed in a Jordanian air strike. But another Yazidi witness has told the BBC that this is not what happened.
Amshe was 17 when she was forced to be a sex slave for Haji Mutazz - the IS number two.
Amshe said he told her Baghdadi was always going to kill Kayla when he had finished with her.
Haji Mutazz laughed when he saw news reports on television that Kayla had been accidentally hit in a coalition air strike, Amshe said.
"Her stupid government," he said. "We killed her."
