Kelly Clarkson Reveals What Her Daughter Said That Made Her Feel Like She ‘Succeeded as a Parent’ (Exclusive)

The singer turned talk show host relocated with her 2 kids from L.A. to New York City for season 5 of her hit show

Kelly Clarkson is feeling settled.

Having just relocated from Los Angeles to New York City for season 5 of her hit talk show, Clarkson, 41, has been building a new life for herself and her two kids, daughter River Rose, 9, and son Remington Alexander, 7 (whom she shares with ex-husband Brandon Blackstock, 47).

“I was very unhappy in L.A. and had been for several years," she tells PEOPLE in this week’s cover story. "I needed a fresh start."

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Related: Kelly Clarkson's Sweetest Mommy Moments with Her Kids River Rose & Remington Alexander

The move has been the right choice for her entire family. “[Remington] walked out of the school here and was like, ‘'This is the school for me. This is better than the last school. This is where I should be.’ And he’s 7,” she says. “So it’s amazing that work is going well, but as a mom, that’s a win for your kid.”

As a mother, Clarkson also admits she “can be hard on myself, but I think I do a pretty good job. I’m definitely not a helicopter mom,” she adds. “I like that they’re independent, but I’m adamant about my schedule, making sure I’m there as much as I can be. There’s no perfect parent; I’m definitely screwing up my children somehow! But I’m doing my best.”

The singer recalls one recent moment with River that did make her feel especially proud as a parent. “She was wanting a dog so we got one and I was like, ‘Well, what do you want to name her?’ And she was like, ‘I want to name her Charlie because Charlie Brown."

Clarkson responded, "‘Okay. Well, some people might think that it's a boy.’ And she was like, ‘What do I care what people think?’ I was like, ‘I'm sorry. Say it again and slower.’ I felt like I had succeeded as a parent.”

Even with Remington, “I had said something and I did not mean to hurt his feelings, but he was like, ‘You kind of hurt my feelings,’ and he voiced himself so clearly,” Clarkson allows.

“I was just so proud of him for using all the correct words and not being overwhelmed emotionally. He just said it so clear and calm. I was like, 'Okay. I could learn something from you today.’ The moments that seem small are really epic.”

The Kelly Clarkson Show airs weekdays. Check local listings for station and time.

For more of Clarkson's exclusive interview, pick up this week's issue of PEOPLE.

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