Sister Annie can be pretty tough to pin down. The narrator never gives a whole lot to go on with this girl. We do know that, from a young age, Annie's a "tomboy and a 'flybie-skybie', as her mother called her" (4.3).
But she eventually grows up and marries a nice guy named Leonard like a proper early-20th-century lady. And she has a close bond with her mother, though the book never really focuses on this bond the way it does with Mrs. Morel's sons (hence the title of the book).
Like her mom, Annie doesn't like Miriam Leivers. Now and then, she guilt-trips Paul for not giving enough of his time and attention to their mother and her. Especially after she (Annie) and Arthur have both gotten married and moved away from home.
When Paul says he's going to end their mother's pain by giving her an overdose of morphine, Annie says it's a totally awesome idea. But it's unclear if she's joking, or if Paul ever goes through with the plan.
Annie also has a streak of cruelty and sadism in her, which we see in the scene where she and Paul sacrifice her doll by burning it: "She was horrified, yet rather fascinated" (4.7). Somehow, she is also disturbed by the fact that Paul "seem[s] to hate the doll so intensely, because he [has] broken it" (4.9).
Annie's doll-burnin' enthusiasm seems to parallel her excitement at the thought of killing her mother, which reveals to us a very dark side in this otherwise minor character. So there might not be much to dear Sister Annie, but what is there is kind of disturbing.
We're guessing Annie was super scarred by her dad, Walter's, violence, and the generally messed up dynamics of her family life. All trauma and little play make Annie a scary girl.