On Monday, Trisha Baker and Debbie Hartman say they were on their way from Orlando, Florida, to Asheville, North Carolina, to see their father in hospice care. Baker said she was seated in the middle of the plane and Hartman toward the back.
As the plane waited on the tarmac -- Baker said it was experiencing GPS difficulties that needed several minutes to be fixed -- she received a text from her brother saying that her father was not expected to live through the night.
Baker said she did not know whether Hartman had received the same text so she went to the back of the plane and sat across the aisle from her sister in a row of empty seats.
"I leaned over to my sister -- I had my seat belt on -- and I put an arm on her leg and I kind of softly told her that Dad wasn't expected to live through the night or that this would be his last night," Baker said.
When Hartman started crying "hysterically," Baker said she reached over. That's when she says a flight attendant sitting behind the pair told her to stay in her seat.
"I said, 'I am in my seat and I have my seat belt on,'" Baker said. "And I said, 'I'm trying to console my sister. We just found out my dad's dying.'"
Baker said the flight attendant replied: "You need to keep your personal problems off this plane."
Although Baker said she was "curt" with the flight attendant, she said she did not curse, yell or threaten her. According to an Orlando Sanford International Airport Police report obtained by ABC News, the flight attendant said Hartman “became verbal and made a hand gesture with her middle finger in the air [at the flight attendant].”
Baker said she did tell the flight attendant that she was being "very rude."
"[I said,] 'We just found out my dad's dying and you're not showing any compassion,'" Baker said. "And she said, 'I'm doing my job,' and I said, 'Well maybe you're in the wrong job.'"
After that comment, Baker said, the flight attendant called the plane's captain. The plane returned to the gate and Baker and Hartman say they were ordered off. Their father died Tuesday. The two sisters said he did not want a funeral.
A passenger who witnessed the alleged incident said, "It was completely inhumane and deplorable that everybody was in shock at what actually happened on the plane by the flight attendants."
The sisters said they tried to get a flight Tuesday but were unable to reach anyone at Allegiant. They're also waiting for their luggage to be brought back from Asheville.
Baker said the flight attendant should be fired.
"I don't know why it happened at all. There will never be justice served. I'll never get to say goodbye to my Dad, and he and I were very, very, very close. ... But there's no reason for this, no justification," Hartman said.
Allegiant said in a statement that it was investigating the alleged incident.
"We rely on our crew members to provide and oversee a safe environment for every passenger, on every flight. We expect that authority to be exercised both judiciously and consistently, with empathy and with good judgment. We take this customer feedback seriously and are in the process of conducting an investigation into what occurred," the airline said.
ABC News' David Kerley contributed to this story.