Love says she should have control of Nirvana's music
Former bassist Krist Novoselic and former drummer Grohl say Love is a "prima donna" whose only concern is her own career.
She argues that Cobain, who shot himself in 1994, had been the sole creative force in the band.
But Novoselic and Grohl have hit back, saying that while Cobain was a gifted songwriter, the three formed an equal partnership.
They also claim that Love is not capable of handling her responsibilities in the trio's company that controls the music.
"In truth, her actions are only about the revitalisation of her career motivated solely by her blind self-interest," Grohl and Novoselic said in a letter to fans.
In court papers, they say Love's behaviour is "irrational, mercurial, self-centered, unmanageable, inconsistent and unpredictable".
Love, Novoselic and Grohl currently control the band's music and receive equal royalties through Nirvana LLC, the company set up after Cobain's death.
But Love now claims she was "emotionally distraught" when she signed the contract with the company.
She also says Nirvana's record contract with Geffen should be annulled since they were taken over by UMG and all rights should revert to her.
Blocked
The record company has withheld $1.3m (£886,000) in the band's royalties, she alleges.
Love also blocked the release of a box set because she did not want an unreleased song and potential hit You Know You're Right to be included.
The release of the 45-track box set had been planned to mark the 10th anniversary of Nirvana's multi-million selling classic Nevermind album.
Love's own band, Hole, have performed You Know You're Right live, despite Love's refusal for the original version to be released.
Insight
She is also embroiled in another legal battle to get out of her own record contract with Geffen.
Novoselic and Grohl say Love may be using the Nirvana songs to get leverage in that case, which is "really about securing more money to support Love's prima-donna lifestyle".
In court papers, Novoselic and Grohl said before the band hit the big time, they split expenses, spent countless hours working on songs together and often slept in Novoselic's van when they played in small clubs.
Nirvana were the leading group in the United States grunge scene, with hits including Smells Like Teen Spirit and Come As You Are, after Nevermind was released in 1991.
Grohl has gone on to have success as singer and guitarist with a new band, Foo Fighters, while Love has also carved out an acting career with appearances in The People vs Larry Flynt and Man on the Moon.