Yeah OP, and when you were a kid, you benefitted from this, so your parents could look after you. You’re coming at this from completely the wrong angle. You’ve already benefitted (as a child) from what you think is disadvantaging you now.
You’ve got an enormous chip on your shoulder about being mistreated. You’re not, it’s just people with kids do need time off in the school holidays, and employers acknowledge this or they’d have a staffing problem. You’ve got loads of freedom and luxury, as your wailing about choosing not to get up early on Christmas morning to see your parents shows. Try to enjoy all the freedom: the times outside of school holidays you can take leave, go abroad, etc.
Fortunately if you had a need (eg caring for a dependent), rather than a preference, employers are reasonable enough to respond to that, just as they respond to the needs of people with children or other dependents.
But you seem to think looking after a sick child is some sort of free pass or jolly, so I can see you’re not going to agree.
That aside, the work policy you’ve described is obviously ridiculous. Christmas leave should be on a rotating basis, really, or necessary arrangements made on a case by case basis. But moaning cos you’d just rather not do a drive to your parents’ after 5 or early in the morning doesn’t make your case well.