His family met with Mayor Nutter Sunday to discuss a resolution, and Pawlucy said that on Monday night he, his wife and their attorney met with Gaymon and an unidentified employee of the school district.
He said the 15-minute meeting didn't feature much conversation between his family and Gaymon.
"None of us really said anything," he said.
Instead, the attorney, Wally Zimolong, and the district employee discussed a "safety plan" for Samantha that would be implemented upon her return, her father said.
"Hopefully, the day goes well," Pawlucy said.
He said the family hired Zimolong, but not "to sue anybody."
The Pawlucy family also has been contacted by City Council members David Oh and Mark Squilla and by State Rep. John Taylor. Oh, who said his office is investigating the incident, won't be at the rally but Squilla plans to attend.
"I want to be there and show my support of freedom of speech and in support of working something out between the district and the family," Squilla said.
Taylor, whose district includes the school, expressed concerns about the rally.
"It's going to be a mob scene. I'm not even sure who's organizing all that," Taylor said. "There's things that aren't going to be in the playbook that could happen there."
Taylor said that he had met with Samantha and her family. As of Friday, Taylor said, the parents wanted Gaymon fired. But Taylor said that he wasn't sure the punishment needed to be that severe.
"I think there's got to be a public display of the notion that that was wrong by the teacher, by the principal, by the district," Taylor said. "I'm not sure I'm in favor of these teachers getting fired for one mistake. There has to be a public acknowledgment of what happened there was wrong, that it won't happen again."
On Monday, Richard Pawlucy said that he didn't want Gaymon fired, but possibly "moved to a lower position."
Fernando Gallard, a spokesman for the school district said that the district was aware of the rally but did not know if Superintendent William H. Hite Jr. would be there.
"We welcome their support and are planning to assist with providing traffic control," Gallard said of Samantha's supporters.
Hite, in a statement released Monday, said that the incident had been "disruptive and hurtful" but represented a "teachable moment" for the school and the city. He said that he would join with Nutter and Philadelphia Federation of Teachers president Jerry Jordan to help the school heal from the episode.
Hite expressed support for Pawlucy and Gaymon. "Our efforts will not take away from the hard lesson learned when an educator acts thoughtlessly," Hite said. "We all concur that there is no room for that type of behavior from adults, especially in a classroom."
Conservative talk-show host Dom Giordano, who has been discussing the story on Talk Radio WPHT (1210-AM), said that he didn't anticipate problems at the rally, scheduled to begin at 7:45 a.m., because it was organized by military veterans.
"This is a very disciplined and mainstream group," he said of the rally's organizers.
Information about the rally was posted on the website of Dave Kralle, a candidate for Pennsylvania state representative. Kralle told the Daily News on Monday that he did not organize the rally but planned to be there.
A rally flier on the website claimed that Charles Carroll High School, at Auburn and Edgemont streets, did not have any flags inside and that students did not say the Pledge of Allegiance.
Gallard said that he was not aware of any specifics about "availability of flags or the pledge at Carroll High School" or of any district policy regarding flags in classrooms.
Pawlucy said that he'd heard similar things about the school from his daughter.
"Sometimes they don't fly their flags," Pawlucy said. "There's nothing in the school, nothing patriotic, at least, though there probably is now. I asked my daughter about the Pledge of Allegiance and she said, 'What's that?' "
Contact Jason Nark at email@example.com or 215-854-5916. Follow him on Twitter @JasonNark.