4:30 PM PT -- Reverend Sharpton tells us he has questions about Hertenceia and her motives. He says, "I do not know that this Aunt has legal standing to speak for the family."
He adds ... "When Kimberly asked us for help we responded because she had legal standing as his domestic partner and the mother of his child ... who is the next of kin."
The family of the man who was shot to death in Brooklyn by the NYPD wants Al Sharpton to mind his own business and stay away from the upcoming wake and funeral.
Akai Gurley was gunned down in a Brooklyn housing project stairwell, and the cop who shot him shockingly texted his union rep before calling 911.
Sharpton has gone on the attack, holding a news conference condemning the cop.
But Gurley's aunt, Hertenceia Peterson -- who is speaking for his mom -- tells TMZ, "Al Sharpton came in, put his name on the situation, but has not even made one single call to the parents to Akai." Peterson says all Sharpton sees "is money and political gain and that he is turning the tragedy into a circus."
Kevin Powell, who appeared on the first season of "The Real World" has been helping the family.
She says the family does NOT want Sharpton at Friday night's wake, where the Rev has promised to deliver a eulogy. She also says he's persona non grata at the funeral.
Rev. Sharpton tells TMZ, he's not grandstanding for the cameras and he was asked to get involved by Akai's domestic partner and mother of his daughter, Kimberly Ballinger.
Ballinger tells us, "Sharpton and his team have been supporting us since day one, and we absolutely want him to attend the wake and funeral."