I am a father and also a co-parent and my boy is two years 3 months old.
I take him from the kindergarten Wednesdays and Thursdays, and on those days the caregiver of the kindergarten is putting my son into the mood that "Papa will take you today". On the days that she forgot it, my kid was crying when he saw I was there to take him. Otherwise it was all good.
I feel that using the end of the school day as a switch point is good, because it saves the kid the distress from from separating from the mother to go to father and vice-versa. They are just coming from a neutral environment (the school), and you dont break them in the middle of an attachment (to the other parent).
About changing weekly or daily, I dont have experience on that, just theory. In both cases, I believe it will take the kid some time to get along well with that.