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 longtime 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 .