Kelly Clarkson Will Make Sure Her Children Grow Up in a 'Stable, Loving Environment,' Says Source

For more on Kelly Clarkson and her divorce from Brandon Blackstock, pick up the latest issue of PEOPLE, on newsstands Friday

Kelly Clarkson has been open over the years about the emotional wounds she suffered because of her parents' difficult divorce — and the star is determined not to repeat their mistakes.

Back in Los Angeles with her children, daughter River Rose, 6, and son Remington Alexander, 4, after self-isolating in Montana with estranged husband Brandon Blackstock, the star — who filed for divorce from the music manager on June 4 — is staying busy while navigating the big changes in her life.

"She had to work through a lot of hurt from her childhood," says a source close to Clarkson, 38, whose emotional 2015 song "Piece by Piece" was written about her father's abandonment and the stability she found in Blackstock, 43.

Added the source, "Her priority is making sure her children grow up in a stable, loving environment."

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Kelly Clarkson/Instagram

Kelly Clarkson and Brandon Blackstock. Art Streiber/NBCU Photo Bank/NBCUniversal via Getty Images via Getty; Taylor Hill/Getty

Since the start of her relationship with Blackstock, Clarkson has been close with his children, Savannah, 18, and Seth, 13, from a previous marriage.

"She's always thought of Seth and Savannah as her own too, and she has a special relationship with both of them," says the source. "Kelly wants to remain close with her step-kids."

In a recent interview with Glamour UK, the Voice coach got candid about abandonment issues she still faces stemming from her childhood.

"I don't think you get rid of that. I have people in my life that suffer from addiction to certain things and that doesn't go away. It's always there," she said. "It's just navigating your life around that existence in your life."

Kelly Clarkson, Brandon Blackstock, Savannah Blackstock, River Rose Blackstock, Remington Alexander Blackstock, and Seth Blackstock.

Another source previously told PEOPLE that Clarkson and Blackstock have "been like friends for a while," and work demands put a strain on their relationship.

"Things had changed in their marriage and the split was a while coming," says the insider. "They both work so hard. It's nearly impossible to enjoy each other, especially with the children needing constant attention."

For all the details of Kelly Clarkson and Brandon Blackstock's shocking split, pick up the latest issue of PEOPLE, on newsstands Friday.