In a tragic mishap, an IVF clinic mistakenly implanted the wrong embryos into two women—leaving them to carry, deliver, and raise one another's babies for months.

Alexander and Daphna Cardinale knew something wasn't right almost immediately after their youngest daughter's birth. The baby was born with dark hair and darker skin, and didn't look like either Alexander or his wife, he says.

“The room shrank, and I got really dizzy … and everything just went numb,” he said in a video recorded by his lawyer, courtesy of TODAY. “I stayed in that place for a long time.”

Alexander says he commented on the baby's appearance for months, sensing something was wrong and that the clinic had possibly made a mistake. When their daughter was two months old, Daphne ordered a DNA test to help alleviate her husband's fears—but could not have predicted the shocking information that awaited them both: the baby didn't biologically belong to either of them.

According to the Cardinales, the fertility clinic where Alexander and Daphna had gone for in vitro fertilization (IVF) implanted another couple's embryo into Daphna and transferred the Cardinales' embryo into the other woman.

Both couples had been raising one another's babies for three months before learning the truth about what happened. The couples swapped babies back in January 2020, and are now raising their biological children.

The Cardinales are now suing the California Center for Reproductive Health, and the doctor they say is responsible, Eliran Mor.

"This is something that's just changed who we are," Daphna tells PEOPLE. "It's still a daily struggle and will continue to be."

Daphna and Alexander aren't the only family members reeling from the trauma of the disturbing mixup—the Cardinales' five-year-old daughter, Olivia. She had fallen in love with her little sister and begged her parents not to switch babies.

The Cardinales say they were devastated to realize they had missed the first four months of their biological daughter's life while also dealing with the crushing blow of having to give up the baby they'd been raising.

"I found out in that moment that she existed, what she looked like and what her name was," Alexander says. The other couple had named the baby Zoe, and the Cardinales decided to keep it. "It's weird learning the name of your child when you didn't name her."

The Cardinales say the other couple—who declined to be publicly identified or comment on the incident—were, understandably, just as devastated and shocked.

Though the families switched babies to their rightful biological parents, they live close to one another and regularly meet up to spend time together.

"There's no book for this," Alexander says. "There's no person to give you advice. So we ended up just sort of huddling together, the four of us, and it's a blessing that we all are on the same page. We've spent every holiday together since then. We've spent every birthday together since then — and we've just kind of blended the families."