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,

She always wanted her kids to have the best relationship possible with their dad,” a source told People on Thursday.

“Workhorse” Kelly Clarkson kept going during her ex Brandon Blackstock’s private three-year cancer battle because she had no other choice. The Grammy winner, 43, not only had a syndicated daily talk show to deliver, but she was also gearing up to launch her Las Vegas residency at Caesars Palace in July, just weeks before his shocking death.