Natalia Bryant -- Kobe and Vanessa's daughter -- got a five-year extension on her restraining order against an alleged stalker ... and now, her mom and siblings are included.
According to court documents, obtained by TMZ Sports, a judge ruled on Monday that the order would be extended for the foreseeable future ... and agreed to modify it to include Vanessa, Bianka, and Capri as protected people.
She initially filed to extend the order back in November .