Well yes, she could, and did, and now she needs to pay the fine she knew would be due, and get over it!
Or fight it, if she thinks fining parents is ridiculous, or morally wrong, or anything else. That's her choice.
Not being able to take a family of 6 on an Easter break abroad is hardly 'abdicating all rights as a parent', is it? You don't seriously actually think that, right?
You have misunderstood. Read again.