The Kill Bill star and her ex-fiance Arpad Busson have been embroiled in a legal wrangle over four-year-old Rosalind, aka Luna, since 2014, when the French businessman went to court to demand regular access to their child.

An initial deal was agreed in September, 2015, but the former couple has since fallen out again, with Arpad objecting to Uma's request to take Luna with her from their home in New York to Europe while she works on a movie.

The custody case went to trial in Manhattan Supreme Court on Friday (13Jan17), and during the first day of proceedings, court-ordered psychologist Dr. Sara Weiss testified about how toxic Uma's relationship with Arpad has become, and noted how little Luna is starting to pick up on the negative vibes whenever they are all in the same space.

"At this point, I don't think these people should be in the same room with each other until they can be more comfortable with each other," she told the court.

Dr. Weiss went on to reveal that although Luna does genuinely enjoy her time with her dad, she suffers from separation anxiety from her mother and therefore should not spend more than seven days away from Uma.

Her suggestion was a blow to Busson's request to have Luna spend two weeks out of her school holidays with him at his homes in London and the Bahamas, although Dr. Weiss claimed longer periods of time in her father's custody would be more suitable when she is older.

She insisted the child currently needs "consistency" during such a key time in her development.

Another point of contention between Uma and Arpad is the actress' decision to send their daughter to the prestigious private arts-oriented Saint Ann's School in Brooklyn, New York, which Arpad does not approve of, according to the New York Daily News.

The trial continues.

Uma and Arpad initially split in 2009, but gave their romance another go and then broke up once and for all in April, 2014. She gave birth to Luna in 2012.