Mel Gibson, Oksana Grigorieva New Court Battle Over Lucia (UPDATE)

6/12/2015 8:42 AM PDT

Mel Gibson, Oksana Grigorieva in New Court Battle Over Lucia

EXCLUSIVE

11:30 PST:  We've learned Mel walked out of court victorious. The judge is allowing Mel to take Lucia to Australia for 1 month and keep her in L.A. an additional 2 weeks before he leaves the country.  

We're also told there was a dispute over which kindergarten school Lucia would attend and the judge sided with Mel.

On the bigger issue of ongoing contention, we're told Mel and Oksana both told the judge they're working on being able to better co-parent.  

Mel Gibson and baby mama Oksana Grigorieva are about to square off in court this morning ... and it's all about their 5-year-old daughter Lucia.

TMZ has learned, Mel is about to go to Australia to do a movie and wants to take his daughter with him for the summer. We're told Oksana objects, so they'll be making their respective cases before the family law judge. 

Our sources say the contention between Mel and Oksana on issues of child-rearing has not subsided ... there are many conflicts. 

And this is interesting ... we've learned Mel is extremely involved in Lucia's life. In fact, the judge has continually increased his custody of Lucia over the years, to the point where he now has physical custody of his daughter slightly more than 50% of the time.