In Act 1, scene 4, why did Claire sell the house and what would be the consequence if she didn't? Was it purely for financial reasons?
I don't think Claire sells the house only for financial reasons. Claire and her boyfriend both have good jobs, so it isn't that she needs the money. Now that Robert has died, Claire feels responsible for Catherine, wanting her to move to New York with her and her boyfriend. Claire has worked extra hard to pay off the mortgage to the house because she knew her mentally-ill father wouldn't be able to keep up the payments. Claire allowed her father to stay in the family home by making the payments, and now that he's dead, she is afraid that Catherine may have inherited the mental illness of their father. She feels she needs to take care of Catherine, just as Catherine took care of Robert. By selling the house, Catherine thinks Claire will have no choice but to move with her. If she doesn't sell the house, Catherine will stay there, and Claire will not be able to look after her. Claire is afraid to leave Catherine alone.
I agree about Claire wanting Catherine to move forward with her life. It's her chance to give back.
What if Claire was merely trying to get Catherine to think about her future without worrying about obligations? Catherine has spent the last 5 years making a selfless sacrifice, but has she perhaps instead been using that as a reason not to step out in faith? She doesn't have faith in herself, choosing to work "privately" without the risk of others criticising her work if she were to do it in the public forum of academia.
Catherine has been supporting Claire this whole time. Sometimes, especially when there is a chance that a person is enabling the unhealthy choices of someone, that person needs to make some drastic changes.
Claire never really intends to leave Catherine homeless, but she does need to rip Catherine out of her comfort zone to get her to work out her future.
Just a thought...welcoming feedback...