The Veep is under fire by Nina's daughter and granddaughter -- Lisa Simone Kelly and RéAnna Simone Kelly, respectively -- for what they say was Kamala's role in deciding how Nina's estate is now managed, and more importantly ... who's managing it (or not, rather).

The Daily Beast outlined the drama quite well -- noting it all started with RéAnna praising Chloe Bailey's rendition of Nina's song "Feeling Good," which she put out to celebrate Juneteenth. However, it caught some flak ... supposedly for being over-sexualized.

RéAnna defended Chloe, though, by saying ... "Everyone’s coming at @ChloeBailey for her performance of my grandmother Nina Simone’s song “Feeling Good." She added, "But what y’all don’t understand is that grandma was a free spirited woman herself!! She would’ve loved that performance  as much as I do! Relax. Chloe killed it. #NinaSimone"

Chloe seemed to appreciate the shout-out. But, things took a hard left turn, as someone asked RéAnna in her comments why her family would create a Twitter account for her grandmother, who passed away in 2003. That set off a looong stream of bashing.

RéAnna wrote this in response ... "Nina’s granddaughter here. My family doesn’t run her estate anymore. It was taken away from us & given to white people. Our family name was DRAGGED in the media. We get NO royalties, nothing. Wanna hold someone accountable?Ask Kamala Harris why she came for my family #NinaSimone."

You can check out the rest of the thread yourself to get into the nitty-gritty -- but essentially, RéAnna blames Kamala for barring her fam from access to Nina's estate ... not to mention rights to her image/likeness, royalties, creative decisions with the IP and everything else.

RéAnna says Kamala and co. gave all those powers to "white people" ... and she feels like her heritage and ties to her grandmother have virtually disappeared, all because of what Kamala's office decided when they were overseeing this estate/charity case back in 2013.

A bit of backstory -- RéAnna's mother, Lisa, was made administrator of Nina's estate upon death ... but some time later, she was accused of misappropriating funds that were tied to both the estate and a charity set up in Nina's name. That's how Kamala's office got involved -- and in the end, they reached a settlement ... the terms of which RéAnna is shedding light on now ... not to mention Lisa herself, who praised her daughter for "speaking her truth."

As part of the settlement, Lisa was prohibited from associating herself with Nina in what seems to be any capacity -- be it familial or otherwise ... in addition to a de facto gag order forbidding her from talking about Nina. That's why RéAnna is speaking up on the issue.