Kelly Clarkson's "staying strong" but is "heartbroken" for her kids after ex Brandon Blackstock's death, a source tells PEOPLE. The singer and her late ex-husband share daughter River, 11, and son Remington,

The family of Kelly Clarkson’s ex-husband, Brandon Blackstock, is beginning to speak out after his tragic death at age 48. Brandon died on Thursday, August 7, after a private, yearslong battle with cancer. His brother, race car driver Shelby Blackstock, 35, was one of the first in the family to publicly address his passing.

Clarkson is believed to have already filmed audition segments for the upcoming season of “The Voice,” but could bow out of the live shows, said industry insiders.