But Yaeger said it's up to the warden to decide whether an inmate has "extraordinary justification'' to alter the terms of his sentence.
"I don't know how he cannot see this as an extraordinary situation."
Vonda Yaeger was at her daughter's hospice bedside on Thursday and was not available for comment. But her sister-in-law Lori Yaeger told ABC News that Jason would do just about anything to be by his daughter's side, and that the strain of the father-daughter separation is agonizing.
"The time he has left to serve? The 11 months? He's offered to serve double that if they'll only let him be with his daughter when she dies,'' Lori said, her voice cracking.
Jayci, named for her father's initials, has been fighting for her life since she was diagnosed with cancer at the age of 3, seven years ago. But in the past six months, she has taken a severe turn downward.
Doctors declared her condition terminal in October. Last month, they found they couldn't transfer her to a children's hospital closer to her Lincoln, Neb., home because they said she wouldn't survive the trip, Lori Yaeger said.
Jason Yaeger has been allowed three brief supervised visits since the terminal diagnosis last fall, and the visits have prompted remarkable, if short-lived revivals in Jayci's condition, she added.
"When he came home in February, Jayci was not expected to live through the night," Lori Yaeger said. "She improved throughout that whole week. Jason was allowed to accompany her to get a CAT scan. He was able to pick her up and put her on the [examining] table,'' she said, growing emotional.
"And this little girl who could barely lift an arm wrapped her arms around him and held on."
As Jayci's health has see-sawed from stable to the brink-of-death time and again in the past few months, her parents have been filing request after request for either a temporary furlough or at least a transfer to the halfway house facility an hour from the child's beside.
Jason Yaeger is currently serving time at South Dakota's most minimum security federal prison, a former college campus in the middle of town in Yankton. There is a two-foot fence surrounding the facility, and inmates move freely around the facility, he said.
For now, the Yaeger family uses the telephone as a lifeline, with Jason coaxing and soothing his daughter through the twilight of her young life.
"Jayci has maybe spoken ten works in the last three months,'' Lori Yaeger said. "She opens her eyes and when she looks at you it's as if she's looking through you.
"When Jason called last Friday, they put the phone to her ear. I don't know what the particular conversation they had that day was, but this little body that was so lifeless? This body that couldn't move? Tears started rolling down her face,'' Lori said. "She's still in there."
ABC News Omaha, Nebraska affiliate KETV and reporter Andrew Ozaki contributed to this report.