 -- The parents of a young American being held hostage with her two children by the Taliban say that they are praying President-elect Donald Trump’s dealmaking expertise will win their loved ones' freedom if President Barack Obama doesn't succeed before he leaves office next month.

Jim and Lyn Coleman are lamenting the sad milestone of their daughter Caitlan, 31, missing her fifth Christmas back home with them in Stewartstown, Pennsylvania, this year. Instead, she’ll be spending it in captivity somewhere in Pakistan with her Canadian husband Joshua Boyle and the couple's two toddler sons – all hostages of a Taliban faction.

"I do believe that either the President will get her home before he leaves or will set in motion a process that the next president can do it," Jim Coleman said in an exclusive interview with ABC News’ Brian Ross for ABC's "Good Morning America" on Wednesday.

But with the clock running out on Obama's presidency, the Colemans are pinning their hopes on a new team headed by Trump to bring their family together again.

Their plight could put to a test yet another long-standing American policy once Donald Trump assumes the presidency: that the U.S. does not make deals or concessions with terrorists to gain the release of hostages.

"I would like it to be tomorrow. I would like it to be before Christmas," Lyn Coleman said in the small living room of the family's modest house wedged between tilled Pennsylvania farmland.

But with the daughter they affectionately call "Caity" still in captivity and with the grandsons they have seen but never met, the Colemans did not put up a Christmas tree or decorate their house this year.

"It just aches. It hurts too much, knowing she’s not here," her mother Lyn Coleman said, but adding hopefully, "I would like to transform this place back into Christmas again."

A new video of the couple with their two sons posted by the Taliban online this week, along with other developments such as a letter from Caitlan they received last April, have given the parents some new optimism that their daughter and her family might soon be set free. She and Joshua were abducted while ostensibly backpacking in Ghazni, Afghanistan in late 2012, when she was pregnant with her first son.

Caitlan Coleman and her family are believed to be held by the Haqqani Network, which has been fighting wars since the 1979 Russian invasion and was closely aligned with the deposed Taliban government in Kabul as well as Osama Bin Laden and al-Qaeda. The Haqqani Taliban also held U.S. Army Sgt. Bowe Bergdahl prisoner for five years until he was swapped in 2014 for five Taliban commanders held at Guantanamo Bay.

Unlike the families of other American hostages such as Kayla Mueller, whose parents were blocked by the U.S. government from paying a ransom ISIS demanded, Jim and Lyn Coleman say their government contacts have been tireless and helpful and would not stand in the way of any effort they made to secure their loved ones' release.

But the Haqqani Network has never asked for money for Caitlan and her little boys in four years, despite the fact that kidnapping and ransom are "part of their business model," said one former operative involved in trying to win the freedom of several American hostages held by the group. She is considered a hostage held against her will by the U.S. government even if no ransom demand has ever been made, officials have told ABC News.

In a letter her parents received last April, the second such correspondence from her in the past year, Caitlan was optimistic and upbeat about the future and plans for her family after being held hostage.

A statement read by Caitlan in the new video this week was the first time her family has ever heard any terms stated for her release.

"We have waited since 2012 for somebody to understand our problems," she said, describing their predicament as "Kafka-esque" and that, "my children have seen their mother defiled."

Caitlan Coleman also said that if Obama is concerned about his legacy, "please don't become Jimmy Carter," an apparent reference to the former president who failed to win the release of Americans held hostage in Iran, who were freed once Ronald Reagan took office in 1981.

"We are told that there are Afghans who are prisoners in Kabul that these men care about, and they do not want to be punished. Indeed, they’ve threatened to retaliate. That their group would do us harm and to punish us. So, we ask that you are merciful to their people, and God willing, they will release us," she said.

The Haqqani Network kidnapped two professors at Kabul's American University -- one American and one Australian -- in August after becoming agitated over a senior member of their clan being convicted and sentenced to death last August by the Afghan government.

Days later, Caitlan and Joshua appeared on video for the first time in several years, saying they would be killed along with their young children if any Taliban prisoners were executed by the Kabul government, though they didn't name any specific prisoners.

The execution of the senior Haqqani figure has not been carried out, American and Afghan officials told ABC News this week.

One other American abducted in 2014 is known to be held by the Haqqani Network.

Despite the fact that the Taliban doesn’t typically execute their western captives, ABC News has withheld the names of the other American hostages for security reasons after receiving requests to do so from the U.S. government and their families.

For their part, the Colemans took joy in the fact that the family appeared very healthy in the new video, with the blonde-haired youngsters bouncing in their father's lap, with the youngest boy making faces at those behind the camera while his older brother picks his nose.

"We were pleased that the family looks healthy and well. That's a good thing," Jim Coleman said.

Lyn Coleman, smiling as she spoke of her family so far away, said, "You just want to reach out, you know, and hold ‘em...and that’s very difficult."

Both Caitlan and Joshua Boyle were critical of their captors, which is a departure from most hostage videos and a fact which has puzzled intelligence officials. It is unknown whether they wrote all or part or none of their comments in the new video, but past practice of the Haqqani Network is to script hostages' statements.

Boyle said the captor network is full of "arrogant ignorance," and the Taliban believe that "America killed all the monkeys in their country and the drones are listening to them sleep at night."

Sen. Bob Casey (D-Pa.) said he has worked closely with the Obama White House and FBI's Hostage Recovery Fusion Cell to help the Colemans bring their family members home.

"I have been working to ensure that our Government is working to safely recover their daughter and to push for our foreign partners to do more on her case, as well. I have met with senior administration officials and foreign government officials on the case," Casey said in a statement to ABC News. "We know that Caitlan has a medical ailment, and as this video confirms, she has two small children to care for. It is unconscionable that they continue to be held, and I urge their immediate release."

Lyn Coleman said the long ordeal has made it difficult not to lose all hope.

"Every morning I get up and I think, 'This might be the day that I get the phone call.' And it's Caity's released or I hear her voice. I guess my hopes are very low because it's been so long," the Pennsylvania grandmother told ABC News.

"I know she has to come back... but I'm not sure I'm ever gonna see her again. I'm not sure I'm ever gonna see my grandchildren. So it's gotten very, very difficult for me."