Michelle Branch Says It's a 'Mindf---' to Raise a Baby While Her Oldest Child Prepares for College

courtesy Michelle Branch Michelle Branch

Amid a series of public ups and downs in Michelle Branch's marriage to the Black Keys' Patrick Carney, the "Everywhere" singer-songwriter's three children are doing well.

Last month, Branch posted — then deleted — a tweet accusing her husband, the Black Keys musician Patrick Carney, of cheating on tour while she was home with their 7-month-old daughter, Willie. After sharing the post, the singer-songwriter, 39, was arrested on a since-dismissed domestic assault charge for allegedly slapping Carney, 42. She filed for divorce days later and wrote in a statement at the time, "With such small children, I ask for privacy and kindness."

"I definitely shouldn't have taken to Twitter to say anything. Here I am saying, 'Please respect our privacy,' but I'm the one who said it to the world," Branch tells PEOPLE, over Zoom from her Nashville home, in this week's issue.

(Days after this interview, Branch and Carney filed to suspend the divorce proceedings for six months to work on their marriage, according to Tennessee court documents obtained by PEOPLE.)

Jeff Kravitz/Getty Patrick Carney of the Black Keys and Michelle Branch

While she may have regrets, Branch has long been known for wearing her vulnerability on her sleeve. One month after the dramatic episode, though, she's honest but careful when addressing the situation. "I have to be respectful of the fact that I'm not the only person involved in this. We have very small children," says Branch, who also has a 4-year-old son, Rhys, with Carney, and a 17-year-old child, Owen (who uses they/them pronouns), with her ex-husband Teddy Landau. "I've promised Patrick I won't speak about it publicly."

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As for Branch's kids, they haven't been clued into the drama. "Hopefully, they don't know anything that's going on. I'm getting ready to leave in a week on tour. Patrick's on tour right now," says the musician, whose new album The Trouble with Fever drops Friday, one day after its accompanying concert tour kicks off in Boston. "Daddy's at work, and mom's getting ready to leave for work. I'm going to bring the baby on tour with me because I'm still breastfeeding."

She and Carney welcomed Willie in February, and since then, most of Branch's time has been happily consumed by the infant. "First of all, she's the cutest little baby ever," she quips. "I'm completely obsessed with her."

Willie's father's been on tour with the Black Keys since early July, and as of late, Branch says Owen's been "a massive help" with babysitting. Rhys, on the other hand, tries his best to assist Mom. "He's in preschool, and he's a wild man," she explains. "He doesn't understand that a baby can't play yet. He's like, 'Come on, can we go play?' And I'm like, 'No, she's just a blob. Give it some time.' But it's really sweet to watch him together."

As Branch has been rehearsing to hit the road, she's also been helping Owen research different potential colleges to attend next year. "That's a whole mindf--- for me, to have a 7-month-old daughter and then one going off to college," says the Grammy winner. "If I didn't have the two younger kids to distract me from the fact that my baby is going to college, I think I would be a mess."

She may still view Owen as her "baby," but they're now the same age Branch was during the creation of the 2001 debut album that'd launch her into teenage superstardom, The Spirit Room. Despite appearing as the spitting image of one another, Owen's living a completely different life than Branch was at 17, having left home midway through high school to pursue a music career rather than attend college.

Branch doesn't consider it crucial for Owen to attend college, but she says "they are so intelligent" and independently interested in two potential topics to study: animation and paleontology. "If you were to run into Owen at any given moment, there's a notebook with a million different characters going on. They're constantly drawing," she says. "The world is their oyster... But Mom is calling it now — they're probably going into animation of some sort."

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Having recently earned their driver's license, Owen's been experiencing a new wave of independence, which can be as overwhelming as it is fun, especially combined with college. "I keep reminding Owen that I left home around their same age, and that's the way you learn — trial by fire," says Branch. "You can only prepare kids so much. You give them all the tools they need to survive on their own, and I think Owen is going to be just fine."

College life will be a brand-new experience for Owen, but Branch predicts they'll at least enjoy it more than life at home with a needy infant sibling. "On any given day I'm like, 'Owen, I need to take a shower. Hold your sister, make a grilled cheese for your brother,'" she notes. "So I'm sure Owen will be excited to be out of the house, away from that."

For more from Michelle Branch, pick up the latest issue of PEOPLE, on newsstands everywhere Friday.