Rajon Rondo allegedly pulled a gun on the mother of his children and threatened to kill her during a heated altercation ... and the woman claims their kids witnessed the whole thing.

TMZ Sports has learned 36-year-old Ashley Bachelor, Rondo's former partner and mother of his two kids, filed for an emergency protective order in Louisville last week, requesting protection for her, her son and daughter ... and the story she tells about the alleged incident is scary.

Bachelor says Rajon -- a 2x NBA champ and 4x All-Star -- was playing video games with his son on May 11 ... when Ashley asked the boy to separate laundry. Bachelor says Rajon became enraged and ripped the game console out of the wall in front of the kid.

Ashley says Rajon then continued the destructive behavior, smashing everything from a teacup to outdoor lights and trash cans.

Bachelor says the kids were upset after witnessing their dad losing it, so she tried to "deescalate" the situation. But, she says Rajon responded by making a death threat, allegedly saying, "You're dead."

Rondo temporarily left the home, according to Ashley, before returning about 15 minutes later, when he allegedly approached a back door and began banging on the window with his gun.