The exes continue to battle over custody of their 15-year-old son Rocco, who has been living in the U.K. with his father since December, despite a judge on Dec. 23 reportedly ordering Ritchie to return him home to New York to sort out his living situation in the States.
Per exchanges at the hearing, the exes had apparently neared an agreement outside of court but seemed to have come to blows in the eleventh hour.
At the hearing – which both Madonna, 57, and Ritchie, 47, called into to listen on speaker phone – a judge and the exes' attorneys agreed that Rocco will remain in London for the time being, where he is enrolled in a school chosen by both Madonna and Ritchie, while he lives with his father for the time being.
"No one is disrupting this household . The child is in school; let us try to allow him to go forward in the most normal way," said New York Supreme Court judge Deborah Kaplan. "We're not forcing the child to leave school. His mother isn't asking that."
Indeed, maintaining a "normal" life for Rocco is one point all parties can agree on.
"In almost every conversation, he has stressed to me how stressful [the very public custody battle is]," Rocco's court-appointed attorney said. "He is going to school now, which is a great step forward, and the parents should be commended that they were able to reach this decision ... He's enjoying himself there; he's having a good educational experience; the school seems to be a great fit for him."
And the judge noted she would not yet enforce her order for Ritchie to return Rocco to the U.S., though, as Ritchie's attorney argued: "Rocco is of an age where he cannot be physically compelled to [get on a plane] back to New York."
Despite this fact, Madonna's lawyer, Eleanor Alter, argued not returning Rocco was a reckless move in teaching him responsibility.
"He taught his son that obeying court orders ... is not necessarily important. That is one of the most serious things that has happened in this court," Alter argued.
Source: Madonna / Instagram
Coming to a compromise has been a feat for the couple, who have a strained relationship.
"I am happy that time and effort went into the research of finding a school that he is comfortable with ... [He's] succeeding and liking it. The mother hasn't asked that the child be removed from school during this period of time while [custody is resolved]," the judge said.
While the exes' and Rocco's attorneys have yet to come to an agreement regarding his custody, all three agreed that it is best to keep him as much out of the spotlight as possible and, if possible, settle the matter out of the courtroom.
"I'm encouraging the parents to continue to resolve this matter in the best way possible for the child to take this tremendous pressure off their son," the judge said.
Madonna and Ritchie are expected in New York court for their next hearing this summer, tentatively scheduled for June 1, after Madonna's camp amend their complaint and Ritchie's and Rocco's lawyers have time to review the amendment.
The exes were originally expected in court Feb. 3 before the date was rescheduled the day before.
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Wednesday's hearing comes as Madonna is halfway across the world in between stops on her Rebel Heart Tour. (She wrapped her Asia leg in Singapore on Sunday and will take the stage in Auckland, New Zealand, on Saturday.)
The custody battle has been boiling for almost three months. Rocco had been on tour with his mom, 57, when he decided he wanted to stay with Ritchie, 47, out of rebellion and because he prefers his dad's more laid-back parenting style and misses his U.K.-based friends, a Ritchie source told PEOPLE in January.
Last month, a Ritchie source told PEOPLE Madonna visited Rocco in London, "hoping to persuade Rocco to come back to New York" – to no avail.
But just days after the visit, Rocco was pictured allegedly smoking, which, per a source close to the singer, left his mother concerned.
"This is exactly what Madonna has been afraid of," the source told PEOPLE at the time. "He needs guidance and direction from his father."
The exes finalized their contentious divorce in 2008 when Madonna agreed to pay Ritchie a settlement between $76 million and $92 million. Before their split, the pair lived together on the historic Ashcombe estate, the same country property where Ritchie married model Jacqui Ainsley last summer.