Friday's surprise announcement that the American Idol judge and her husband are splitting came "after months of nonstop arguing," a family told People.
"Marc and Jennifer decided it's best to go their separate ways for the sake of their two kids," the source told People in a Monday report.
"Jennifer is doing okay... in the past two weeks, she has spent a lot of quality time with her kids and her family in L.A. She is, of course, sad that she and Marc didn't work out, but they both feel they have tried everything."
According to Us Weekly, the couple's reconciliation attempts including counseling.
"[Jennifer] tried everything she could to make it work," a source told Us, explaining that the couple's relationship had been rocky for years. "They went to marriage counseling. She was patient and loving and did everything he wanted her to... She exhausted all the possibilities."
"She is devastated... Absolutely beside herself. This is someone she dedicated a long time to, and that she truly loved."
However, despite their feelings for each other, Lopez and Anthony's relationship had reportedly been bumpy from that start.
"They had a very up and down marriage," a second source told Us. "They would get into heated, horrible fights. Then, they would also go through times where they were extremely loving and romantic...It was a roller coaster with them from the beginning."
Lopez and Anthony announced their split in a brief joint statement released late Friday afternoon.
"We have decided to end our marriage," they said in the media statement. "This was a very difficult decision. We have come to an amicable conclusion on all matters."
"It is a painful time for all involved, and we appreciate the respect of our privacy at this time."
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Lopez and Anthony were wed in 2004 and have two children together, three-year-old twins Max and Emme. The wedding was the second for the 42-year-old Anthony and the third for the 41-year-old Lopez, who previously had brief marriages to Ojani Noa and Cris Judd.
While there has not been an official announcement yet, E! News recently reported that Lopez -- who joined American Idol as part of last season's judging shakeup alongside fellow judge Steven Tyler -- has agreed to return for Idol's upcoming eleventh season.
According to prior reports, Lopez received $12 million to serve as a member of Idol's panel and was seeking an increase to return (unlike Tyler, who signed a multi-year-contract, Lopez's judging deal was only for one season).
While Lopez had suggested her busy schedule would prevent her from making a future commitment to Idol, InTouch Weeklysubsequently reported Anthony's desire to have her spend more time with him was the real cause of her hesitation.
"Jennifer signed a one-year contract with an option to renew," a source told InTouch in its July 4 issue. "She's ready to commit to a few more seasons because she loves the job and the money, but Marc wants her to quit so she can spend more time with him."