I’d argue the main part of the argument isn’t the ad hominem. “For the betterment of society” works in this argument and it doesn’t really focuses on the mother, it just makes her realize that this is a real situation that she herself should know personally.

It does address using taxpayer money to lock up violent criminals is beneficial for society and supporting and without going in to depth, it also argues that the idea of student debt repayment would also be a net positive for society.

Sure, it’s not a detailed argument but it’s also not playing on guiltiness by blood relation saying she should be locked up as well.