This is something I used to deal with during my second marriage. I was lucky enough to be able to write my own schedule at the grocery store bakery,But I would get up early and take light rail into town, drop my son at preschool, and walk over to work. Then after my shift I’d go and pick him up right before they closed. (Wife at that time commuted with our one vehicle).
Chores we’d split in time we had. Managing stuff is hardest when kids are little or with multiple kids.