Rosanne Cash is opening up about the highs and lows of growing up with her superstar father, Johnny Cash.

In this week’s issue of PEOPLE, the singer-songwriter remembers the toll her father’s meteoric rise to fame in the 1950s and ’60s took on their family life.

“My childhood was chaotic, number one,” Rosanne says. “I understood from a really young age that [my dad] was an artist and that his mind worked differently. And … that scared my mother.”

Rosanne grew up mostly in Southern California, where her mother Vivian Liberto and father moved from Memphis with their growing family in 1958. Two years earlier, Johnny had written his hit “I Walk the Line” about Liberto’s fears that he would stray on the road. (Liberto’s suspicions later came to fruition when Johnny struck up an affair with fellow country star June Carter.)

Suspecting Johnny’s affair with Carter, who was part of his touring ensemble, Liberto filed for divorce in 1966. Two years later, Johnny married Carter after he got clean.

Despite the circumstances of how Carter’s relationship began with Johnny, Rosanne says she felt no resentment towards her new step-mother.

“It seemed inevitable, though it was so painful for my mom. I had two really good examples from women in my life. My mom gave me this powerful sense of discipline, family, mothering and detail orientation. And June gave me this sense of expansiveness and how to live life as a performer.”

Despite some lingering resentments about her father’s absences during her childhood, Rosanne says they were healed after her father asked her to join him on stage one night to sing “I Still Miss Someone.”

“He worked out all his problems onstage, and that happened with me that night with him. It just all got fixed.”