Nipsey Hussle Family Claims Tanisha is Negligent Mom, Shouldn't Get Custody

Nipsey Hussle's family has a new argument for why they should retain custody of his daughter -- they claim there's ample proof her mother is unfit, based on her 2 other children.

Sources close to the late rapper tell TMZ ... his family's lawyers think they can win the custody battle for his 10-year-old girl, Emani Asghedom, by highlighting Tanisha Foster's track record with her 18-year-old daughter.

We're told the girl is currently in juvenile detention in L.A., and has been in and out of the system since she was 12. Our sources say she's in juvi now for petty theft, and nobody will come forward to claim her ... including Tanisha.

Even though her daughter is 18, we're told the detention center won't release her because she doesn't have a GED or a stable environment to which she can return. Our sources say Tanisha's been MIA most of her daughter's life and has refused to attend her court hearings.

We're told Foster also has a 17-year-old son who bounces around from home to home and doesn't attend school regularly.

Nipsey's family claims the proof is in the pudding and feels Foster is not a fit parent -- and definitely isn't qualified to care for Emani.

We broke the story ... the family also believes Foster is unstable due to her long rap sheet and current legal issues.

Emani is currently living with Nipsey's sister, Samantha, who kept custody of her after a court hearing last month ... much to the chagrin of Tanisha.