A source tells PEOPLE in this week's issue that the superstar "didn't think it was in her best interests to stay with" the former MLB player

Just a month after putting on a united front with Alex Rodriguez amid a swirl of breakup rumors, Jennifer Lopez is officially moving on.

While the superstar and the baseball player turned entrepreneur released a joint statement on April 15 announcing the end of their engagement, multiple sources confirm in this week's issue of PEOPLE, on newsstands Friday, that it was Lopez, 51, who ultimately broke up with Rodriguez, 45.

Listen below to the episode of our daily podcast PEOPLE Every Day for more on Jennifer Lopez and Alex Rodriguez's split.

"She insisted on it. There are are too many issues that are unresolved," says a friend of Lopez, who has been filming her upcoming comedy Shotgun Wedding in the Dominican Republic over the past few months.

In the end, the sources say, Lopez could no longer fully "trust" Rodriguez, who flew to visit her in the Dominican Republic days after they publicly acknowledged on March 15 they were working through long simmering issues.

"She has been pretty miserable," says the friend, "and didn't think it was in her best interests to stay with Alex."

While the former couple — who got engaged in the Bahamas in March 2019 after two years of dating — appeared to be in a good place as they celebrated Lopez's performance at President Joe Biden's Inauguration in Washington, D.C., in January and then Valentine's Day in February, sources say they'd been quietly struggling for some time as the COVID-19 lockdown exacerbated existing issues.

"They both liked spending more time together as a family, but it was difficult to keep that special spark when they saw each other every day," another insider says of the couple, who were forced to cancel two wedding ceremonies because of the ongoing pandemic.

Jennifer Lopez, Alex Rodriguez
Jennifer Lopez and Alex Rodriguez
| Credit: ANGELA WEISS/AFP via Getty Images

Then, when Lopez headed to the Dominican Republic for work, rumors Rodriguez had a wandering eye added strain.

While sources say infidelity wasn't the cause of their breakup, "whether or not he has cheated doesn't matter," says a music source. "She won't tolerate the fear of it in the air between them."

In the wake of their breakup, Lopez and Rodriguez are figuring out how to untangle their intertwined worlds. Over the years, Lopez's 13-year-old twins Max and Emme, with ex-husband Marc Anthony, and Rodriguez's daughters Ella, 13, and Natasha, 16, with ex-wife Cynthia Scurtis, have grown close. ("Our kids have become best friends," Rodriguez previously told PEOPLE.)

While the onetime power duo, dubbed J-Rod, also have several business ventures together and share properties in New York, Los Angeles and Miami, "they're especially sad for the kids since they are all so close," says the Lopez friend. "It's not a good situation but inevitable."

For now Lopez is focusing on what brings her the most joy: her kids and her work.

"Jennifer has been in these difficult situations before. She is not one to sit around and cry," says the friend. "Her kids make her the happiest. She is doing well."

Jennifer Lopez and Alex Rodriguez
Jennifer Lopez and Alex Rodriguez with their kids
| Credit: Alex Rodriguez/Instagram

She's also found support in Anthony, 52, who recently brought Max and Emme to the Dominican Republic to spend quality time with their mom.

"Jennifer and Marc have a great relationship," says the friend. "Having him around while she has had to work abroad has been very comforting."

Though ending things with Rodriguez wasn't easy, Lopez feels at peace with her decision.

"They will try to be friends, and there is respect there," says a Miami source. "But they are definitely going their separate ways."

For all the details on Jennifer Lopez and Alex Rodriguez's split, pick up the latest issue of PEOPLE, on newsstands everywhere Friday.