So if I understand correctly, you both want them on the first day of school? Here is what I would suggest, tell her that you want them on the first day of school as well, so since both of you want them then you'll have to fall back on the schedule to resolve this which means you will have them. Then tell her if next year the first day of school falls on your week again that you will let her have them to be fair.
It's important to be flexible when you can be, because in the coming years there will be many times when you both need to alter the schedule because you're on a work trip, or sick, or planning a vacation, etc. XW and I have worked with each other a lot on schedule modifications and never had a conflict we couldn't negotiate. The decree called for one of us to have the kids over Thanksgiving and the other over Christmas, and it would flip back and forth each year. But in actuality we've always worked it out to where we both get to see them on every holiday.
