Frances was "devastated" after she found out her ex-junkie mom handed over Kurt's private journals to the Museum of Style Icons in Newbridge, County Kildare, Ireland.
The 26-year-old musician and model appeared without Courtney, 54, in July at the launch of a rare exhibition of her Nirvana frontman father's personal possessions at the museum.
But after she finished her publicity duties, a "seething" Frances flew into a rage at Courtney for allowing the diaries to be included as part of the show.
"Frances and Courtney reunited after years of rows and estrangement, and now, sadly, they've fallen out again," a source told Radar.
"Frances didn't know until the last minute Courtney was giving Kurt's diaries to the museum and Frances was devastated she had revealed such private documents."
Added the source: "She told Courtney she was just using Kurt for publicity again and has virtually stopped speaking to her again."
The two have kept away from each other publicly for months, and their Instagram feeds are largely absent of shots of each other.
Kurt tragically committed suicide on April 5, 1994, and Frances blasted her mom for sharing the Nirvana rocker's diaries.
"I don't look through his journals — it feels too intimate," Frances said.
"I am really regretful that my mom put those out there. I can't imagine being dead and having people know my intimate thoughts.
What an invasion of privacy — I don't think it is merited," she continued.
"It is a different thing to get to know him through his art, which was a deliberate public extension of himself."
The rare exhibition of Kurt's belongings in Ireland that sparked Courtney and Frances' latest feud will run until the end of September.
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