Lawyer Stephen Kolodny accused Oksana, 40, of lying in a recent deposition - when she allegedly claimed her former lover could only get sexually aroused by beating her - and then leaking her own story about it, conduct he argued is not in the best interests of their daughter.
The judge refused the request for an immediate ruling in the case, and has instead set a hearing for a date in February.
Mel, 55, and Oksana have been locked in a bitter custody battle over Lucia since splitting in April last year.
While the Russian singer has accused her former boyfriend of being physically and verbally abusive toward her, his ex-wife, Robyn –who he was married to for nearly 30 years and with whom he has seven children - has previously defended him.
She told a court last July: “Mel never engaged in any physical abuse of any kind toward me before, during or after our marriage. Mel was a wonderful and loving father."