Rumer Willis' Custody Battle: Ex's Visits with Daughter Will Remain Supervised

Rumer Willis scored a legal victory in her ongoing custody battle ... because a judge ruled her ex's visits with their daughter will remain supervised for now.

A Los Angeles County Superior Court judge ruled that Rumer's ex Derek Richard Thomas' visitation time with their 3-year-old, Louetta, will still be monitored, and the remaining issue of whether he can have overnight visits without a monitor will be addressed at a hearing on September 10.

For now, the judge says both parents should work together to agree on a monitor they trust to watch the visits ... and, if they can't do that, then the judge says a professional monitor will handle it.

As for other issues raised by Rumer ... the judge says she won't rule on them at the hearing, and Rumer should raise them in a different legal filing instead.

We broke the story ... Rumer rushed to court last week to ask the court to require continued supervision of Derek -- claiming he's repeatedly violated custody orders and exercised dangerous judgment around their child.

Rumer claimed Derek had repeated issues with the nannies assigned to supervise his time with Louetta.

Among the incidents described in the filing, Willis claims Derek left the supervising nanny with Louetta at a Fourth of July parade, and later refused to allow her into the Airbnb where he was staying with the child.

She also questioned his judgment around their daughter, claiming Derek wanted to cross a five-lane highway with a 55-mph speed limit while accompanied by Louetta and allegedly chose to walk approximately two and a half miles in extreme heat rather than rent a car.