By Ana Cabrera and Elizabeth Stuart, CNN

Snowmass, Colorado (CNN) - It's been seven months since Dennis Burns has had any contact with his two young daughters. No visits, no Skype, no phone calls, no communication at all.

Just silence.

But all that could change in the next few weeks.

His daughters are victims of an international abduction.

Burns' ex-wife, Ana Alianelli, spirited away the children, 7-year-old Victoria and 5-year-old Sophia, from their home in Colorado and fled to her native Argentina more than 3½ years ago, violating a court order.

"You know I think about them a lot," Burns told CNN in an exclusive interview. "I dream about them a lot. I can feel their little hugs around my body. I just want to hug them back, and it's super painful."

Burns has devoted his life savings and all his time to fighting what's become a messy international legal battle.

His odyssey now appears to be reaching a conclusion: Argentina's Supreme Court has denied the last of appeals by his ex-wife this year, which means Burns has won his case. The final step will be an order of return from the U.S. State Department and a date to transfer custody of the girls to him.

It all began in September 2010, when Burns and Alianelli were divorcing and found themselves at an impasse: Alianelli wanted to relocate to Buenos Aires, and Burns wanted to stay in Colorado.

After a 13-month custody battle, a Colorado judge ruled in favor of Burns, declaring him the primary residential parent.

"I felt a sense of relief that was just beautiful," he told CNN last November, when "New Day" first presented his story. "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."

Just three weeks later, Alianelli flew the girls out of the United States on their Argentine passports. They've been living with her in Buenos Aires ever since.

Messy legal battle

Burns filed an application through the Hague convention child abduction treaty to have Victoria and Sophia returned to him. The Hague treaty is an agreement among countries designed to prevent or resolve cases like Burns'. The U.S. State Department describes it as "a multilateral treaty that provides protection for children from the harmful effects of abduction and wrongful retention across international borders." In theory, children should be returned within six to eight weeks after a Hague application is filed and a court gets the case. Argentina became a signatory country in 1991.

Despite the treaty, Burns' case has taken years to resolve. The Argentine court system allows for multiple appeals, which is exactly what Alianelli has done, dragging the case on for years. Two appellate courts ruled in Burns' favor. The last ruling was on New Year's Eve.

"The Supreme Court of Buenos Aires ruled for the return of Sophia and Victoria, which is fantastic and was really, really good news to bring in the New Year for me," he said.

Six weeks later, on Valentine's Day, Alianelli filed what would be her final appeal to the Supreme Court of Argentina. It has meant more waiting for Burns, but the Supreme Court of Argentina has ruled in his favor, and that court's decision is final.

Alianelli and her lawyers have declined several requests for an interview to get her side of the story. Instead, they provided this statement: "No comment."

Meanwhile, Burns was supposed to be allowed at least three Skype communications with his daughters each week - under court order - but he has been completely cut off by Alianelli.

"We're getting closer to justice being restored, and this is her way of getting back at me, I guess," he said. "But it's punishing them more than me. It hurts me, but they're children who need their father and their mother."

Taking the fight to Washington

Burns has joined forces with the hundreds of other American parents enduring the same heart-wrenching situation, taking their battle to U.S. lawmakers in Washington. Notably, he's working alongside David Goldman, who has been in Burns' shoes.

Goldman fought for more than five years to bring his son, Sean, home to the United States from Brazil. During his ordeal, U.S. Rep. Chris Smith, R-New Jersey, played an integral role in helping Goldman. Since then, Smith and Goldman have worked together to develop new legislation in the hopes of resolving parental abduction cases more quickly.

"Where's the enforcement? Where's the ruling? Every day is a day lost, every day is a day you can't get back, and we have to do what we can," said Goldman.

House Resolution 3212 is a bill designed to ensure that countries comply with the Hague abduction treaty. The bill outlines more than a dozen steps that the U.S. State Department could take, including the threat of sanctions, when a Hague country does not hold up its end of the deal.

The legislation has the potential to affect thousands of U.S. parents. The State Department reports more than 1,000 children were internationally abducted by a parent in 2013 alone.

The bill passed the U.S. House in December.

"It was beyond expectations," Smith said. "It was unanimous: 398 (yes votes). Totally bipartisan."

The bill now sits in the Senate Foreign Relations Committee, which held a first hearing on the proposed legislation on February 27.

"If HR 3212 was already a law, my daughters would most likely have been not only returned by now but probably would have been returned in the first year of this unending nightmare," Burns said.

The final legal decision

Now that Argentina's Supreme Court has ruled that Victoria and Sophia should return to the United States, Burns is in what he hopes are the final weeks of his nightmarish journey. Even after his daughters are back in his care, he vows to continue to help other parents fighting the same battle.

Burns hasn't had any communication with his girls since last July, and he realizes that he will never get back the precious moments he's missed out on for the past 3½ years. He also says he's concerned about how his ex-wife may have characterized him in the years since his girls were taken.

However, Burns remains determined and steadfastly hopeful that he'll be able to say these words to his daughters, in person, someday soon:

"Papa loves you, Victoria and Sophia. I love you very much."

CNN's Melissa Kondak and Michael Martinez contributed to this report.