One of the biggest problems with seniority rules workplaces is that it is the lower seniority people who have small children and generally need the most flexibility.
That's why, as a senior driver, I try to show a little consideration and keep my personals focused on things really important, not just a day off to drink beer.
As for this OP, if you have received prior approval for this day off stand your ground. That child will only have one day in her life that was their first day of kindergarten. There will always be another day at work.