T.,
Lots of parents set up their custody schedule based on what works for them and the child. Would it be possible for her Dad to take her from Friday night till Sunday night, or from Saturday morning (if he'd like a night to be free) and take her to school Monday morning?
I don't know if you live in the same town or school district, but a friend of mine used to alternate weeks, switching on Friday afternoon. One week with Mom, then one week with Dad. I'm not suggesting this, since you want her to be with you during the week, it's just an example of the variety you can find.
Do you and her father get along okay? If you do, talk to him about why you want to make the change, and focus on how you feel it will benefit your daughter. If there are issues with his schedule, work together to find something everyone can live with, and try to plan the switch with enough lead time for everyone to settle any changes to their schedules that need to be made. It's really all about cooperation, if you have an open line of communication.
If you don't get along, then you have to do what you do for everything. Go through whatever intermediary you use to communicate, expect a fight just for the sake of having one, and then go through whatever conflict resolution process is necessary, and be prepared for the possibility that you may not win.
Best of luck. This stuff is so hard on everyone.
Jess