The Tyrone family has no strong parent figure to take responsibility for the care of its members. Without supportive parents, the children are left to look after themselves and their parents, and they're simply not cut out for the responsibility.
Psychologists might say none of the Tyrones has a good support network. The father acts childishly most of the time, and the eldest son, at least, doesn't look up to him. This son, Jamie, is the character who requires the least caretaking, but that's really because both he and his parents think he's a lost cause. The younger son Edmund, meanwhile, is the sickly baby of the family. He's clearly the parents' favorite and can't seem to put his adult life in order. If you're looking for helpless characters, though, his mother gives Edmund a run for his money – she has to be coddled and protected from herself and the family's anger.
There's a weird vacuum, then, at the top of this family, with no respected leader and lots of people who demand help and care. The failure to take familial responsibility is a real problem in Long Day's Journey, as none of the characters has anyone they feel they can turn to in times of need.
Cathleen is as much a member of the family as Jamie, and certainly more instrumental to its (limited) stability.