France vs. America: Inside Scarlett Johansson and Ex Romain Dauriac's Custody Battle Over Their 2-Year-Old Daughter

Scarlett Johansson officially filed for divorce from French husband Romain Dauriac on Tuesday. Both are seeking residential custody of their 2-year-old daughter, Rose Dorothy Dauriac, and now, the former couple are gearing up for what could be a difficult legal battle.

“He plans to petition the court to allow him and his daughter to move to France,” Dauriac’s lawyer, Harold Mayerson, tells PEOPLE. “He believes that her schedule makes it impossible for her to have [primary] physical custody.”

In a statement, Johnasson said: “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. 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.”

A legal expert tells PEOPLE Johansson’s hectic filming schedule could work as a disadvantage to the actress.

L.A.-based family law specialist Steve Mindel — who does not represent Johansson or Dauriac — says the court will begin by assessing which parent has a more stable living environment for their daughter, and “is going to want to keep the child in that kind of stable living arrangement.”

“The courts really have to try to design a program that works for the child as well as for the parents,” he said. “The court is going to look at this and say, ‘Okay, what are the travel schedules of both parents?’ “

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But a second legal expert argues that since Johansson’s career has been “consistent” since the child’s birth, her travel schedule will not play a large part in the custody battle.

“When you’re a couple, you share responsibility. Most people delegate responsibility at certain times in their lives,” New York family law attorney Marilyn B. Chinitz tells PEOPLE. “He doesn’t get to go back to France with the child simply because he’s been caring for her while Scarlett is doing movies. That’s not sufficient. That’s a transient, temporary scenario. And the court looks to deeper levels of commitment to the child — the stability, the security, emotionally, financially.”

Instead, Chinitz says the court will look to determine where the child has more significant roots.

“Where have the parties resided? Where is the child attending pre-school? Where is the child’s pediatrician?” she says. “The connection that the child has to a particular jurisdiction is critically important. So the court doesn’t care where mom or dad are born. It’s what the connection that the child has to a particular state.”

Mindel, who notes that the New York courts will likely have jurisdiction over the matter, says that the court can end up taking an active hand in imposing the conditions of the custody arrangement.

“Notwithstanding the fact that the child doesn’t live in the jurisdiction, the court can impose a lot of conditions — one party pay the travel expenses of the other, the child have frequent contact by Skype and telephone calls, that the child is transported back and forth between the United States and France or France and the United States, depending upon where the child is,” he says.

And Rose’s young age, Mindel explains, makes things a bit easier for the court.

“Because the child is not in school yet, the court can be very flexible with the schedule,” he says, noting that “it’s probably better for the child to spend a lot of time with both parents, so the courts may not set up a situation where the child is with one particular parent most of the time.”

Regardless of where the child lives, both parents will have time with the child.

“The child is always going to have some time share somewhere with both parents,” says Mindel.