"They really tried," a source tells PEOPLE, "but sometimes it's best not to be married"
Attending the Stand Up to Cancer benefit on Jan. 28 in Los Angeles, the pair arrived separately but joined up inside the intimate event, sitting together in the center of the room and betraying little sign of an imminent split.
But behind the scenes, the Oscar-winning actress, 41, and the Coldplay frontman, 37 – who announced on Tuesday their decision to consciously uncouple – had been struggling for some time to keep their marriage afloat, several sources tell PEOPLE.
The pair, who are parents to daughter Apple, 9½, and son Moses, 7½, “really tried to make the marriage work, but sometimes it’s best to not be married,” says a source close to Paltrow. “They know that about each other now.”
Rumors of trouble had long dogged the couple, and Paltrow acknowledged facing challenges in her marriage.
“You’re not learning anything unless you’re having the difficult conversations,” she told Self last year. “Dealing with things directly changed my relationships. Sometimes when you get clear about who you are, others get less comfortable because they liked who you were. It’s changed my marriage, too, but he’s up for the challenge.”
As for cheating rumors, the source close to Paltrow says she finds the chatter “ridiculous. And you know what? She doesn’t care what people think. She really doesn’t, she knows the truth.”
“They have worked really hard for a year or more, going to therapy, trying to make it work – and she’s been more honest than ever about how hard marriage is – but they just decided it was best to not be together anymore as a couple,” adds the source.
Distance and competing work schedules were always a challenge for the pair, who had long divided their time between their homes in London and Los Angeles. Martin has been working on his new album with Coldplay and recently signed on as a mentor for NBC’s The Voice, while Paltrow wrapped her film Mortdecai in January and recently reprised her role as Holly Holliday on the 100th episode of Glee.
After traveling to the U.K. for Christmas, they had spent much of the past several months in L.A. and appeared “very together” during awards season, says an industry source, turning up at the Golden Globes on Jan. 12 and at Sean Penn’s Help Haiti Home party the night before.
Away from the spotlight, both Paltrow and Martin have prioritized parenting. “They made an effort to be there for their kids at their activities, and though they had killer schedules they were always around together in L.A. and a united front at parties in their Brentwood neighborhood,” says a source who knows the couple.
“They weren’t a traditional couple per se, but they were a couple and tried to do anything any family would do, from carpool to a lemonade stand.”
Despite the news of their split, both stars are united in their effort to keep the children’s lives as steady as possible even as the rumor mill churns.
“They are both prepared for the next few weeks and what people are going to say and they really don’t care,” says the Paltrow source. “It will pass; [Gwyneth] knows that.”
“They are still a family. They will always be a family. Nothing will ever change that.”
• Reporting by JENNIFER GARCIA, JULIE JORDAN and ELIZABETH McNEIL