Thousands of miles from New York, Monica Lozada-Rivadineira's family in Bolivia is stunned by her killing and eager to resolve who will get custody of her 4-year-old daughter, who was abandoned on the streets of New York City.

Relatives recall a happy, independent woman who in 2001 left Cochabamba, a Spanish colonial city in Bolivia, full of hopes for a better life.

"Her dream was to save up money in the U.S. and come back to Cochabamba to open up a business and buy a house," said brother Jaime Rios Rivadineira, 24.

Seated in his family's modest living room in Cochabamba filled with framed school awards, Lozada-Rivadineira's brother leafed through a photo album with pictures his sister sent from New York, each with a handwritten note on the back.

"We're at a water park, the mural behind us makes it look like we're sitting with seals, and my shirt is stained with ice cream," Lozada-Rivadineira wrote on the back of one photo showing a smiling Valery in her arms.

Offers to adopt the child have poured in. For now, Valery is staying with a foster family in Queens. A family-court judge will decide who she will live with permanently.

As for custody of Valery, Rios Rivadineira said his family wants to honor choices his sister would have wanted, which might mean Valery's staying in the United States.

"We don't want to take away the dreams Monica had for her," Rios Rivadineira said. "She lived for her daughter, worked for her, so she didn't lack for anything."

The 26-year-old woman vanished Sept. 24. New York police said she was killed by her boyfriend. Valery was found early Sept. 25, wandering barefoot.

Desperate to find relatives, U.S. officials took the unusual step of putting the child on television. Soon the plight of the girl and her missing mother captured the attention of people across the United States. On TV, the girl described her mother as looking "like a princess."

On Thursday, police searching a Pennsylvania landfill where New York trash is hauled said they found a woman's corpse. Police said they thought it is that of Lozada-Rivadineira.

Cesar Ascarrunz, 32, is being held without bail on charges of strangling the woman, dumping her body in a pile of trash and abandoning her daughter to the streets, New York authorities said.

Valery's paternal grandmother said she doesn't want the custody contest for the girl to "be like the one for the raft boy, Elián (Gonzalez)." Several relatives — including both grandmothers — hope to raise her.

"The little girl is not a trophy," Ana Maria Rivera said. "She is not a territory."

Rivera, said she would be willing to raise the child along with Roxana Rivadineira, the girl's maternal grandmother, who plans to travel to New York from Bolivia.

Valery's parents brought her to the United States as a baby. When the marriage broke up, her dad, Juan Carlos Saavedra, 25, returned to Bolivia with the couple's younger child, a son, and Lozada-Rivadineira moved to the Queens section of New York with Valery.

But Rivera said her son, who is imprisoned in Bolivia on drug charges, wants Valery raised alongside little brother Juan Carlos, 3.

Roxana Rivadineira is set to arrive in New York in the next few days.