How does the apartment building itself create problems for the Younger family as they begin the day? Since the family has to share a bathroom they fight over the bathroom.

From the text:

Moreover, a section of this room, for it is not really a room unto itself, though the landlord's lease would make it seem so, slopes backward to provide a small kitchen area, where the family prepares the meals that are eaten in the living room proper, which must also serve as dining room. The single window that has been provided for these "two" rooms is located in this kitchen area. The sole natural light the family may enjoy in the course of a day is only that which fights its way through this little window.

It is morning dark in the living room. TRAVIS is asleep on the make-down bed at center.