Bruce isn't allowed to have a favorite child. His children will riot.
Bruce also isn't allowed not to have a favorite child. His children will riot.
Therefore, Bruce has a rotating schedule:
If there's one person who hates Mondays as much as Bruce, it's Tim. They quietly suffer together. Monday belongs to Tim.
Somehow Tuesday is even worse than Monday. Bruce requires an emergency dose of optimism, terrible puns, and his first baby bouncing into the Cave. Tuesday belongs to Dick.
Cass has dance class (if she's in Gotham at the time), and Bruce wouldn't miss watching her perform for the world. Wednesday belongs to Cass.
Damian spends Monday through Thursday finishing his newest art project, because in his mind taking an entire week for anything is for the weak.
Also, Thursday is the day Damian decides Bruce is required to accompany him to a cat café or for ice cream.
Why Thursday? Because Bruce traditionally did father-child outings on Fridays, and Damian wanted his own day.
Jason stays the longest on Fridays. He would come and raid the pantry, the library, then he stays for dinner and for family night.
Bruce treasures every extra hour he gets with his son, even if Jason is only here for the free food.
Steph believes Saturdays were invented for causing problems and shopping, and somehow always convinces Bruce to pay for whatever she wants.
This is entirely her fault because she refuses to use the allowance card Bruce keeps trying to give her.
Sunday belongs to his Sunshine. No further explanation.
Everything is subjected to change because his children are gremlins. So if anyone annoys Bruce on their day, favorite-child status is immediately transferred to:
A. whoever called him "Dad" most recently.
B. whoever hasn't given him a headache lately
C. whoever hugged him last.
Alfred, meanwhile, has exactly one favorite grandchild. It's Jason, and he admits it out loud.