Is it permissible for my sister to use my brother's wife's laptop in her absence, knowing that she would not mind? And if it is not permissible, what should she do about the times she has used it; should she seek forgiveness and repent or not, and should she inform my brother's wife and ask for her forgiveness, or should she repent between herself and Allah?

Customary permission is like explicit permission. So, if the husband's and owner's consent is known through custom, then their permission is granted even if they do not speak. Consequently, there is no objection to your sister opening your brother's wife's device unless she is explicitly prohibited from doing so; because an explicit prohibition negates customary permission.