A topsy-turvy international child custody saga ended when a Mexican judge allowed a teenager to travel to Texas with her mother, a month after sending the wrong girl to the United States.

Dorotea Garcia and her 13-year-old daughter, Alondra Diaz Garcia, smiled as they left the court in the western state of Michoacan, walking between throngs of reporters and entering a police car to be taken to the airport.

"We're going to the United States. We're very happy," Garcia said next to her black-haired daughter whom she had not seen since her then-husband took the girl to Mexico without her consent eight years ago.

The judge, Cinthia Elodia Mercado, gave custody to Garcia after DNA tests confirmed her identity on Thursday. The father, Reynaldo Diaz, voluntarily brought the daughter to Michoacan over the weekend.

Mercado had not asked for a DNA test last month when she ordered another girl, Alondra Luna, 14, to be sent to Houston after Garcia thought she was her daughter because they had a similar facial scar.

The case captivated Mexico after a video emerged of Luna being dragged out of her school screaming by police in the central state of Guanajuato.

Luna was sent to Houston even though she and her family insisted that she was not Garcia's daughter. She spent four days in Texas until DNA tests showed she was the wrong girl.

Luna and her family traveled to Michoacan on Friday to confront the judge in Los Reyes.

"Open the door and listen to us! We want an explanation," Alondra Luna shouted while her father angrily banged on the courtroom door.

Luna's family has threatened to take legal action.

"We want the judge to show her face and explain to us the treatment they gave us in April, when they kidnapped my daughter knowing that she was not the one they were looking for," said her father, Gustavo Luna.

Despite its pleas, the Luna family was not seen by the judge and left the court after half an hour.

"We will proceed legally against the judge and ask for them to pay for the harm they've done," Gustavo Luna said.

- Emotional reunion -

The judge spoke to reporters on Friday but did not address the the Luna family's protests as she closed the case.

"The minor (Alondra Diaz) expressed from the first moment that she wanted to be with her mother, the mother who made the request," Mercado told reporters.

The mother and daughter had an emotional reunion on Tuesday as they saw each other for the first time since 2007.

To resolve the custody dispute, Dorotea Garcia agreed to withdraw charges against the father for taking the girl away without her consent.

"I'm sad for everything that has happened," Alondra Diaz told the US Spanish-language network Univision this week, adding that she was not angry at her father.

"I was happy with my dad. But at the same time I felt like something was missing," she said tearfully. "I was missing my mother's love."