By Elizabeth Stuart and Ana Cabrera, CNN

Snowmass,Colorado (CNN) - For Dennis Burns, images of his two young daughters bring him both joy and heartbreak. He's spent the past three years missing out on the everyday simplicities that most parents take for granted. Three years of no Christmases or special occasions with Sophia, now 4 years old, and Victoria, who just turned 7.

The reason for his ordeal? His ex-wife, Ana Alianelli, abducted them from their home in Snowmass, Colorado, and took them to Argentina in defiance of court-ordered arrangements.

Burns is now what is known as a left-behind father, embroiled in an international legal battle until he is granted permission by an Argentine court to bring his girls home. In the meantime, all he can do is wait.

"There's times when I want to think about them, but it hurts too much to think about them," he told CNN in an exclusive interview. "There's things that I need to do to survive in this marathon of a situation that I'm in, to keep my mind focused on my goals that I need to - to try to get them back."

Burns once had a charmed life - a successful real estate career, a wife he met on the ski slopes of his beloved Aspen. They were wed in 2004, but after five years of marriage, their relationship soured.

"When we first realized we were going to get a divorce, we had a very heartfelt conversation," he said. "But we both agreed that we were going to be amicable for the sake of the girls."

But their divorce proceedings were far from amicable, made even worse by Alianelli's allegations that Burns abused her, and by her request to relocate with the children to Buenos Aires, Argentina. Burns objected that the move would make him "just an acquaintance, not a father."

Her claims of abuse against Burns were unfounded, and after a 13-month custody battle, a Colorado judge declared Burns the primary residential parent and ordered that the children stay in the United States.

Burns said that was one of the happiest days of his life.

"I felt a sense of relief that was just beautiful. And I was like, 'I'm going to be able to spend time with my daughters, finally, and live with them and be able to teach them things, and show them things, and live here with them in Colorado,' " he told CNN.

Just three weeks later, in September 2010, his girls were gone. They've been in Argentina ever since.

A parent's worst nightmare

There are currently thousands of similar unresolved international custody cases in the United States, and the U.S. State Department receives about 1,200 new cases each year.

Argentina is one of the more than 80 signatory countries of the Hague Convention on the Civil Aspects of International Child Abduction, a 1980 treaty by which nations work together to solve international abduction cases quickly.

According to the treaty, the first custody hearing is supposed to be held six to eight weeks from when the applications to have the children returned are filed. Burns' first hearing was in December 2012, more than two years after Victoria and Sophia were taken. That it has gone on so long only adds to the emotional trauma for the children.

"When a child is ripped from their home environment, their friends, their families - they begin to identify with their abductor," said Burns' lawyer Caroline Langley, who specializes in child abduction laws and has expertise with Hague cases.

"The psychological trauma to the children starts on that slippery slope where it's very, very difficult to pull them back from being so aligned with the abductor," she told CNN.

Now, to see his daughters, Burns must travel to Buenos Aires at his own expense - a trip he's made seven times. And when he does visit his girls, he brings a witness.

"For Dennis' protection, we always make sure that somebody goes with him, someone from the embassy, a neutral third party," Langley said.

A visit rudely cut short

Burns invited CNN to accompany him on a recent visit with his daughters in Buenos Aires. The crew watched from the car as Victoria and Sophia excitedly opened the gifts their father brought them.

A few minutes later, Alianelli and several lawyers interrupted the visit - serving Burns and Langley with general criminal charges "against women and children" - without providing a reason why or evidence to support the charges.

And when they saw the crew filming, Alianelli's attorney swatted away the camera. The crew quickly left, catching a quick glimpse of Victoria and Sophia in tears. Burns was devastated by what had transpired in front of them.

"So, my visit with my girls now was a total of maybe about five minutes, 10 minutes, and then the ambush came out," he said.

CNN reached out to Alianelli and her attorney, Daniel Mercado, to hear their side of the story. They didn't want to talk. Instead, Mercado provided a statement in Spanish, saying "Ms. Alianelli does not wish to make a comment with respect to the case."

Legal limbo and financial upheaval

For now, Burns must wait for the legal process to take its course. An appellate court in Buenos Aires ruled in favor of him bringing Victoria and Sophia back to the U.S., but Alianelli appealed the decision. Burns is now waiting for the Supreme Court of Buenos Aires to hear his case.

A website has been set up to seek support for Burns' cause and raise awareness about international child abduction. It includes a petition urging the government of Argentina to honor the U.S. court ruling and return Sophia and Victoria to their father's custody. The website also asks people to press their members of Congress to pass a bill, introduced in October, that would strengthen safeguards against international child abduction.

Burns says the financial strain has forced him to file for bankruptcy and foreclose on his home. He now lives in a one-bedroom apartment filled with photos of his daughters in every room, on every wall. Their tiny coats still hang on hooks near his front door.

In the meantime, Burns' entire family in New Jersey also is desperate to get the girls back home. His mother, Marie Burns, says she cries every time she sees a girl who looks like Victoria.

"A little girl comes in (a restaurant) with her dad or her family and happened to look like Victoria and I'm sitting there eating with a friend, and suddenly, I'm bawling," she said.

Another dad offers encouragement

Burns has now enlisted the help of another American dad who knows exactly what he's going through: David Goldman.

Goldman's 5½-year journey to get his son, Sean, returned from Brazil after he was abducted by his mother drew international attention. His description of how Sean is doing, since his return in 2009, gives Burns hope.

"He's thriving. He's playing lacrosse, he's playing basketball on the travel team," Goldman said. "He just came home yesterday and they had their (school) pictures. He's 5-foot-9 - he just turned 13 and he's 5-foot-9."

Burns says he dreams of the days when his life can go back to normal. Until the Buenos Aires Supreme Court hears his case, all he can do is dream of what that will be like.

"I don't have the opportunity with them to get them out of bed in the morning, make them breakfast, take them to school," he said. "I just want to be able to know that they are there every day and be able to hug them and love them."