The reality-TV personality, who insists that her engagement to Casey was real, is scheduled to be grilled by King on Tuesday during a live, in-studio appearance...
"The Johnsons just want Tila to go away," source said. "They're in mourning. She is the last thing they want to deal with right now."
Earlier this week, cops were called when Casey's longtime friends Nicky Hilton and Bijou Phillips showed up at Tequila's home to collect the late Johnson & Johnson heiress's two dogs and other belongings, including clothes and insulin shots.
"Everyone knows the tabloids won't back away from Tila, but they didn't think Larry King would actually consider having her on his show," the source said. "They've called him and sent him emails asking him to cancel the interview."
Another source tells me Tequila is supposed to be the only guest for the entire one-hour show, which is planned to be a "tribute" to Casey: "It's going to be all the good things and happy times of her life."
Reps for King, Tequila and the Johnson family did not comment.
Check out the late heiress and some of her famous friends in our Who Was Casey Johnson? photo gallery.