My kids have been in Montessori school since 14 months old, and I didn't take their first day off as I needed to be at my school for my students. I guess I'm confused as to why you need to take the day off? Drop off should be quick as lingering around usually adds to stress and anxiety for children, and sometimes for the parents too - LOL!
I don't get personal days in my school board - we are not allowed to take any personal days off whatsoever, whether it be a wedding, honeymoon, first day of school, etc. so I have no experience with this at all as it's not part of our school board culture here. Even personal days were available to me, I absolutely wouldn't
waste a whole day for this as drop off is short - what are you going to do for the rest of the day? I don't want to offend you either, but I agree with your colleague as well in that you should be at your own school on your first day of school. You can make the night before special, or, have a special breakfast the morning of the first day and then everyone can be on their way. I don't get the whole 'special' aura that surrounds the first day of school, anyway. Don't get me wrong, I love school as I am a teacher, but for us, it's just a regular day like all of the other regular school days in the year (my kids also go to school in the summer, so they don't get the whole 'Back to School' stuff either).
I wish you luck in whatever you decide - I hope your daughter has a great day at school and that you have a great first week back to school.
Tiger