Is Nora justified in leaving her husband and children in A Doll's House? (provide quotations)
This is necessarily a subjective question. Nora has good reasons for leaving her husband and children, that is beyond doubt. However, the question of whether or not these reasons justify her departure must be answered according to your own opinions.
Making an argument justifying Nora's decision, we can point to 1) the demeaning treatment she receives from her husband, Torvald and 2) the idea that Nora feels there is no way for her to develop into an individual while living with Torvald.
Throughout the play, Torvald demeans his wife, perhaps lovingly, yet consistently. He refers to her with pet names that associate her with helpless woodland creatures.
Her husband constantly refers to her with pet names, such as "singing lark," "little squirrel"...
He also bars her from taking any responsibility in the household beyond dealing with the children. She is treated, by him, like a child herself. (She must follow his rules.)
Importantly, Torvald also expects that Nora will agree with him on all matters of importance. His opinions are to be her opinions.
This is the final reason that Nora cannot remain in his house (and it is hishouse.) When she realizes that she should expect more from herself than the life she is living as the powerless wife with no identity of her own, Nora feels forced to leave her family.
When Nora confronts Torvald with the truth of how he has treated her and limited her development as an adult, thinking person, he attempts to remind her of her duties.
Helmer: Before anything else, you’re a wife and mother.
Nora: I don’t believe that any more. I believe that before anything else, I’m a human being, just as much a one as you are … or at least I’m going to turn myself into one.… I want to think everything out for myself and make my own decisions.
In this difference of views, we see one justification for Nora's choice. If Torvald feels that she is a wife and mother before she is a person with opinions and feelings of her own, how can Nora expect to grow into something more than a functionary filling these roles?