It was a revelation the family found "disturbing," according to a lawyer.
Beresford-Redman's sister told "Good Morning America" that the idea that her brother-in-law might have been capable of such a horrific crime saddens her.
"I think everybody can be capable of murder. And I'm really sad if he did," Carla Burgos said. "She was a very, very pleasant person."
An arrest in the case has been delayed, pending forensic testing, but Monica Beresford-Redman's family said it wants justice immediately.
"We want the person that murdered my sister," Jeane Burgos said. "I want this person in jail to pay for the rest of his life for what he did."
Burgos said she doesn't believe Beresford-Redman's story that his wife disappeared after she left by herself to go shopping.
Police officials said there is no record of her having left the hotel grounds.
Security guards check all cars that come and go.
Her husband was initially arrested after authorities found scratch marks on his body, and witnesses said they heard the couple arguing the night she disappeared.
He has since been released but has been ordered to stay in Mexico until the investigation is completed.
"It's just like horrible, it's just like so hurtful," Jeane Burgos said. "I can't even express how much pain is inside my body."
The couple's two children, Alex and Camilla, are back in Los Angeles. A judge has granted temporary custody to their father's parents, but their maternal grandparents are fighting for custody.