@madonna / Instagram 1 / 9
@madonna / Instagram 1 / 9

Just a few years ago, Madonna would have been celebrating Mother's Day -- today marks the annual holiday in Great Britain -- with her four kids, including eldest son Rocco.

Instead, sources say she's privately admitting defeat and inching closer to a custody deal over the teenager as her bitter feud with ex-husband Guy Ritchie rages on.

According to Page Six, Madonna, 57, and the British director, 47, are close to a deal to decide how much time Rocco -- who's been with his dad in London since December -- will spend in Britain with his dad vs. in New York City with her.

"She's basically accepted she's not getting Rocco back," an insider tells Page Six. "But she's holding out to get him back for one weekend per month."

The news comes four days after Madge and Guy's lawyers went head-to-head before a Manhattan Supreme Court judge on March 2, and three days after the case was heard in London's High Court.

The American judge scolded Madonna and Guy, who both phoned into the NYC proceedings. "Frankly, both parties have chosen to live their lives in a very public way and may welcome the publicity, but the child has not," the judge said, according to Page Six. "He would like this matter resolved, and the issues concerning him and his family, in the most private way possible."

The next day, a British judge also warned them both to push themselves "to reach an amicable solution."

According to another report, this one in Britain's Mail on Sunday, Madonna has privately conceded defeat over custody of 15-year-old Rocco. She's told friends she's "lost the battle," the newspaper reports.

"The fact is Madonna has now accepted Rocco isn't coming home and that his home is now with his dad. Rocco wants to be with his dad but she won't give up being his mother," one of Madge's close friends told the Mail on Sunday. "She won't stop fighting to try to make sure Rocco is kept safe and has what he needs. She can't understand why it has come to this. Her world has been shattered."

The reports follow yet another emotional outburst from the pop queen, who broke down on stage during her March 4 Rebel Heart Tour stop in Auckland, New Zealand.

Amid tears, reports the Daily Mail Australia, she told fans, "There is no love stronger than a mother for her son," then dedicated her performance of "La Vie en Rose" to Rocco.

In a video of the episode obtained by TMZ, she can be heard telling the crowd, "It's a love song for a man, but I know he'll be one, one day. I hope he hears this somewhere and knows how much I miss him."

If negotiations fall through, Madonna and Guy's legal teams are due back in court in New York on June 1 and in London on March 10.