There’s a custody battle brewing between Scarlett Johansson and her estranged husband Romain Dauriac.
According to Dauriac’s lawyer Hal Mayerson, Dauriac wants their 2-year-old daughter Rose to live with him in his native France.
Mayerson tells PEOPLE that the actress, 32, who travels often for work, is pushing for “hybrid schedules and changing schedules.” In her divorce filing, Johansson asked for primary residential custody.
“No mother or father wants to be the drop-in babysitter for the other parent,” Mayerson says.
In response, Dauriac is fighting for joint custody and primary physical custody, in addition to “economic relief” for child support and counsel fees.
The Ghost in the Shell actress previously said that she will “never” open up about their split.
“As a devoted mother and private person and with complete awareness that my daughter will one day be old enough to read the news about herself, I would only like to say that I will never, ever be commenting on the dissolution of my marriage,” the statement reads. “Out of respect for my desires as a parent and out of respect for all working moms, it is with kindness that I ask other parties involved and the media to do the same.”