Shaunie O'Neal's lawyers just fired off a letter to Shaq's people, claiming the bball star "interrogated" the couple's children to tell him everything they knew about her new man ... "to the point that they felt intimidated and scared of him."
Shaunie also claims Shaq told their 6-year-old son to tell her boyfriend that Shaq "is going to kill him" -- and that Shaq even screamed at the kid and said, "Say it now! My daddy is going to kill you!"
Shaunie's lawyers are demanding Shaq halt "further inappropriate discussions" with their children -- which is an alleged violation of the non-disparagement provision of their divorce judgment.
TMZ asked Shaq's attorney for a comment, but he hasn't gotten back to us.