HOMESTEAD, Fla.—Rick Hendrick set history in motion over milk and cookies served on a plate donned with Mickey Mouse ears.

In a snack setting designed for children, the car owner called Jimmie Johnson and Chad Knaus together to discuss the strain in their relationship following their failed 2005 championship run. If the two couldn’t stop bickering like little kids—and Hendrick wasn’t convinced they could—he was fully prepared to split them.

“It was getting to the point where Chad and Jimmie were having more bad days than good days,” Hendrick said. “I called them into my...

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