When I worked PT in a law firm and DH was full time we had a deal that if ine of the kids needed collecting early from day care he did it. The way I saw it I was only there 3 days a week so needed to be really there on those days. He did all pick ups. I took care of the rest on my days away from work. However if one of the kids was sick I stayed home. If they were going to be home for a 2nd day then DH stayed home.
That's how we worked it. Wasn't a perfect system and if either of us had to be in court then it was basically paper rock scissors.