If she obtains a legal divorce, then certainly Nora will be able to remarry. In 19th century Norway, however, both parties had to consent to the divorce, so what if her husband refuses?
If she is Catholic, she cannot have a church wedding unless her first marriage is annulled, and since she has three children, it is unlikely that the church would declare her marriage unconsummated. She could have a civil ceremony or be married in a Protestant church.
Her first husband would have custody of the children, not only because she initiated the divorce but also because she abandoned them. She would also lose all rights to whatever property she had brought into the marriage, since only husbands could own land.
Negative attitudes toward divorced women carried over into the 20th century. When Edward VIII of England had to step down from the throne of England when he married Wallis Simpson, a twice-divorced woman.