Estranged husband Daniel Giersch countered in L.A. Superior Court with papers alleging the actress, who's four months pregnant with their second child, has a bad temper, once throwing a laptop at him and another time trying to sock him with her fist.
Rutherford, 40, filed for divorce from Giersch, an entrepreneur, last month after being married a little over two years, seeking sole physical custody with monitored visitation. On the same day, Giersch filed for legal separation, seeking sole legal and physical custody with visitation for her.
In emergency papers filed Jan. 9, Rutherford sought to bar Giersch, 34, from traveling outside the United States with their son Hermes.
Views As Risk"I feel there is some risk that he will leave the country with Hermes and I will not know where they are," Rutherford said in a declaration, adding that during their marriage, he told her of a pending investigation in his native Germany that could lead to his arrest.
Rutherford also asked the court to allow her to travel to New York for work with their son.
Giersch fired back in a response that he has dutifully served as Hermes's main caretaker in L.A., and that Rutherford's commitments to Gossip Girl and her bicoastal commute were a reason why their marriage failed.
"I have been extremely concerned about our son living in a hotel and a New York lifestyle, and this has been one of the main reasons, if not the reason for the ending of (Rutherford's) and my marriage," Giersch said.
He added: "(Rutherford's) routine is that she has weekly hair appointments for at least two hours, manicures, pedicures, shopping and the like. She has been able to do all of that because I have been taking care of Hermes, and am happy to continue doing so, as it would be best for him."
Cites TemperRutherford further claimed in her declaration that Giersch has a bad temper, saying he "has a history during our marriage of getting angry with me and leaving, without telling me where he is going."
Giersch responded that the actress is the one with anger issues: She "has tried to hit me with an open fist when she's had an angry outburst. On July 6, she threw a laptop computer at me while we were in Hamburg. She smashed the computer on the table and it broke."
A judge has denied Rutherford's request regarding travel with Hermes, but set a court date of Jan. 21 to further hear the matter.
Through his lawyer, Fahi Takesh Hallin, Giersch told PEOPLE, "Ultimately I want both of my children to have a stable environment." A lawyer for Rutherford had no comment.