Story Via TMZ - Nipsey Hussle's first baby mama will object to the appointment of the rapper's brother to administer his estate, and might even ask that SHE be appointed administrator, if the hearing goes down as planned, and millions of dollars are on the line ... sources connected to the case tell TMZ.

Sources connected to Tanisha Foster tell TMZ, she will not accept Sam Asghedom, Nipsey's brother, as the manager of the late rapper's fortune, which Sam estimates at $2 million. Sam filed legal docs, saying Nipsey died without a will, and he wants to be appointed the administrator of his brother's estate. A judge is set to rule on Sam's request June 10.

Under California law, Nipsey's children would share equally in his estate. In addition to 10-year-old Emani, the child Nipsey had with Tanisha, he left behind 2-year-old Kross, who's mother is Lauren London. So, each would get around $1 million, less fees and taxes.

Tanisha is fighting for custody of Emani, and if she's successful, she would have some power in handling the money and would probably be entitled to use some of it to provide for the child. A judge has temporarily blocked Tanisha from having physical custody of Emani ... the child is currently living with Nipsey's sister.

Our sources say Tanisha has tentatively decided to ask the probate judge to continue the hearing so she can get clarity on the custody case. We're told there is bad blood between Tanisha and Nipsey's family, and she will almost certainly end up objecting to Sam becoming the administrator.