Will a custody order dictate who has to transport the kids?

My ex and I have 3 kids and they are all very gifted, both academically and athletically. They are enrolled in numerous school activities and sports, and we spend most days of the week running back and forth between their various activities and games. Also, I live in Fairax but my ex lives in Richmond, and only sees the kids on the weekends. He does, however, attend most of their events. Can he be required by court order to assist in transporting the kids to some of their activities, since he’s coming to Fairfax and attending them anyway? I can barely keep up getting all 3 to all of these events and it isn’t fair that I have to by myself. I’ve asked him to help out but he refuses.