"They want to spend time in person to figure out their life together," a source tells PEOPLE of the power couple, who reunited in the Dominican Republic on Sunday

Jennifer Lopez and Alex Rodriguez are committed to giving their relationship a real chance.

After a weekend that saw the power couple confirm news that their romance has been on shaky ground, they reunited in the Dominican Republic — where Lopez has been filming her upcoming romantic comedy Shotgun Wedding — on Sunday to work through their issues.

"Alex flew to the Dominican Republic, and Jennifer was excited to see him in person," a source close to Lopez tells PEOPLE in this week's issue, on newsstands Friday. "They want to spend time in person to figure out their life together."

In a brief statement on March 13 — hours after a swirl of breakup rumors hit the internet —Lopez, 51, and Rodriguez, 45, admitted they've been "working through some things" in their relationship.

"The past few days were upsetting and stressful," says the Lopez source. "She and Alex have a lot of issues they hope they can work through, but they both seem willing to do whatever it takes to stay together."

While the superstars appeared happy as they celebrated Lopez's performance at President Joe Biden's Inauguration in Washington, D.C., in January and then Valentine's Day last month, sources say they've been quietly struggling for some time.

"She's been contemplating breaking up with Alex for six months," says a Lopez friend.

In her February Allure cover story, Lopez told the magazine that she and Rodriguez had recently sought couples' therapy.

"I think it was really helpful for us in our relationship," she said, adding that they had hit pause on wedding planning after being forced to cancel two ceremonies due to the ongoing COVID-19 pandemic.

Around the same time, speculation Rodriguez had had an affair with Madison LeCroy, 31, a cast member on Bravo's South Carolina-based TV show Southern Charm, arose after the hair stylist alleged she had exchanged direct messages and spoken on the phone with the retired baseball player-turned entrepreneur. But the Lopez source maintains that "Madison has no bearing on the rough patch."

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While Lopez and Rodriguez fell quickly in love four years ago, sources say the honeymoon phase faded over the last year in lockdown.

"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," the Lopez source says of the couple, who have two children each (Lopez shares 13-year-old twins Emme and Max with ex-husband Marc Anthony, and Rodriguez shares daughters Natasha, 16, and Ella, 12 with ex-wife Cynthia Scurtis).

Jennifer Lopez and Alex Rodriguez
Jennifer Lopez, Alex Rodriguez and kids
| Credit: Alex Rodriguez/Instagram

When Lopez headed to the Dominican Republic for work, the cracks in their union grew deeper.

"Filming during COVID has been very hard for her," says the Lopez source, adding that in addition to missing her children deeply, "not having Alex around all the time makes her stressed."

While Rodriguez visited Lopez last month, the "distance has been an issue," adds the source. "Jennifer was very unhappy." Similarly, a friend says Rodriguez was "in a mood" when he returned home to Miami after the trip.

Though the current situation has been stressful for both stars, sources say they recognize how much they have to lose. At the top of the list is the happily blended family they've built over the last four years. "They've been trying to keep it together for the kids," says the Lopez source.

Lopez first met Rodriguez at a Yankees game in 2005, while she was still married to Anthony, 52. It wasn't until 2017 that the pair reconnected during a chance encounter at a Beverly Hills restaurant.

"I saw him as he passed by," Lopez previously said on The Ellen DeGeneres Show. "Afterwards, I went outside, and for some reason I felt like tapping him on the shoulder."

After chatting, Rodriguez made the next move: "He texted me, said, 'Let's go out to dinner,' and I said, 'Okay,'" Lopez said.

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Credit: Jason LaVeris/FilmMagic

With initial shared passions for business and philanthropy, the couple — who announced their engagement in March 2019 after two years together — bonded further when they took the important next step of introducing their kids.

"I was so loving to his kids, and he was so loving and accepting of mine," Lopez told People in 2018. "They embraced each other right away. [It was], 'I get a new bonus brother and sisters!'"

As they face the possibility of a split, Lopez and Rodriguez are considering the impact. In addition to merging their families, they also have several business ventures together — including a joint deal with wellness brand Hims & Hers and with the sunglass brand Quay — and share properties in New York, Los Angeles and Miami.

"They're tied in their business worlds so it's not a cut and-dry breakup," says the Lopez friend. "It's taken a while for them to even think about untangling it all."

Adds the Lopez source: "They invested a lot into their relationship. An official split would be devastating on so many levels."

Jlo and Arod
Alex Rodriguez and Jennifer Lopez
| Credit: Karwai Tang/WireImage

With weddings plans now on an indefinite hold and the status of their relationship up in the air, Lopez and Rodriguez are hoping that the time they're spending together in the Dominican Republic will help get them back on track.

"They love each other," says the Lopez source, "and they have so much to lose if they split."

For all the details on Jennifer Lopez and Alex Rodriguez's fight to save their relationship, pick up the latest issue of PEOPLE, on newsstands everywhere Friday.