The 41-year-old musician - who has a 22-month-old daughter Lucia with the 'Braveheart' star - has reportedly claimed that 14-year-old Alexander, whose father is actor Timothy Dalton, has been affected by their violent row last year, in which Mel allegedly knocked out two of her teeth.
According to gossip website TMZ, Oksana has also claimed her former partner was abusive to her son during the argument, scaring him so much he hid under the bed, and on another occasion threw him onto a table - allegations which Mel denies.
Mel and Oksana are currently in the process of organizing a custody settlement for Lucia, and met with a judge and mediator separately last Friday (12.08.11) to discuss the details.
In March, Mel pleaded no-contest to a charge of battery against Oksana, and has already completed the community service aspect of his sentence.
In addition, he is currently undergoing a year-long course in anger-management and having domestic violence counselling.
Following a number of leaked recordings of their rows appearing online, in which Mel was alleged to use violent, abusive and racist language towards Oksana, the 55-year-old star played down the tapes.
Mel - who claims he slapped Oksana during a row when she became hysterical and he feared for the safety of Lucia - has said: "You have to put it all in the proper context of being in an irrationally, heated discussion at the height of a breakdown, trying to get out of a really unhealthy relationship.
"It's one terribly, awful moment in time, said to one person, in the span of one day and doesn't represent what I truly believe or how I've treated people my entire life."