Claire is a practical woman who likes to take charge. She left to make a life for herself in New York, while Catherine had to quit school to stay home and care for her father. But, Claire did send money to her father and Catherine so they could pay off the house. It's not as if she abandoned the two of them totally. Claire seems to have taken her family responsibilities seriously. I think Claire is very jealous of the relationship between Catherine and their father. Catherine inherited her father's genius for mathematics, and Claire doesn't fit into this world that her father and Catherine share. Claire felt he belonged in an institution, but Catherine totally disagreed. Along with dad's mathematical genius, Catherine seems to have inherited his madness as well, and Claire now believes it is her responsibility to take care of Catherine. Perhaps this is guilt because Claire left? Claire is also the one who seems convinced that Catherine is insane, but even though there are signs, we don't know for sure if this is the case. Does this make Claire a controlling, cold, and insensitive person? I don't think so. She just doesn't know how to relate to her sister, perhaps because they never developed a relationship with each other. Catherine was her father's confidante, not Claire's. There's no doubt that resentment exists on both sides, but underneath it all, I think Claire cares about her sister and wants to do what she feels is best for her.
Claire is often insensitive, and somewhat calculating, but she does not do it to be malicious. Claire has her family's best interest at heart, but she is not skilled at softening her approach.
Claire lived in a small, studio apartment to work and pay off her family's mortgage. She sacrificed her own creature comforts for the family's happiness.
While Claire and Catherine do not get along, Claire truly believes that Catherine would be better off moving to New York. Catherine believes she just enjoys interfering, but Claire really wants the best for her sister.
Claire also believed that both her father and family would be better off by putting their father in an institution. Claire is not being intentionally cold and unfeeling, she thinks it is the most practical solution.
Claire is shown to be a little insensitive and cold as that is the way she shows her care and concern for Catherine. But, she is not calculating. Claire views herself as the most responsible and mature in the family, thus, she always tries to take charge of the situation. She does not believe in other people's views, especially Catherine's. She treats Catherine like a little girl, instead of a young woman. This is why Catherine dislikes Claire and views her as pushy and irritating.
One reason that Claire acts this way is because she views Catherine as unstable and fragile, feeling that Catherine has "some of [Robert's] tendency...towards instability". However, Claire is not completely at fault. The way Catherine acts in Act 1, Scene 2 would, from Claire's point of view, show that she is abrasive and crazy. After all, Claire did not witness whatever happened in Scene 1, so, based on Catherine's contradictory and downright absurd answers to Claire's questions, she would think that Catherine needs professional help.
Throughout the novel, her view of Catherine does not change. In Act 2, Scene 2, even when Catherine insisted she wrote the proof, Claire still refused to believe her sister was capable of such things. In fact, she did not justify her disbelief and in Claire's opinion, Catherine's abrasiveness and possessiveness of the proof would show her instability. Claire also shows her distrust of Catherine by cutting Catherine off or plain ignoring her whenever she tried to answer Claire's questions about the proof. For example, she asks Hal to "tell [her] exactly where [he] found [the proof], to which when Catherine answers, she tells her to "hold on" and continues to press Hal for answers. It shows that Claire would rather trust a stranger rather than her sister.
Right in Act 1, Scene 2, we see Claire already taking charge and pushing her opinions on Catherine. When Claire asks "how do you take [your coffee]", despite Catherine replying, "black", Claire ignores her and tells her to "have a little milk". Soon after, she pressure Catherine, questioning her about her decision not to wear the dress she bought, not using the conditioner. Throughout the novel, she pressures Catherine to come to New York as Claire feels she needs to be taken care of.
Claire is also shown to be very efficient and pragmatic. Right in the morning, she had already planned out Robert's funeral (Act 1, Scene 2). "I thought we'd have some people over tonight." She ordered "some food. Wine, beer." and insisted that "it would be alright" when Catherine objected. Also, in Act 1, Scene 4, Claire, who was only in Chicago for a few days, was shown to have had already sold the house and was "hoping to do the paperwork this week". Also, her idea of looking after Robert was to place him in "full-time professional care", a direct contrast to Catherine, who wanted to keep Robert at home, taking care of him. In Act 2, Scene 3, she passes the proof to Hal to check its authorship, stating that "it's far by the most convienient option". She does not seem to care or to take the trouble to find the best way to deal with the proof. She simply finds the most convienient way to do things.
Also, Claire is portrayed to be a little cold, based on the way she takes action. She sold the house without consulting Catherine or thinking about Catherine's emotional attachment to the house and Robert. She does not care much about the proof either: "Take it. I don't care" (Act 2, Scene 3).
What do you think?
Claire is the only responsible adult in the family. When her father was alive, she supported her entire family to "humor" his desire to be at home and Catherine's desire to enable the situation.
She's continuing in this role beyond her father's death because she's been forced into it all along. it's only natural.