All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
We shall answer your question in the following points:
Firstly, there is no religious impediment to the woman's work in lawful fields that do not involve Shariah violations. There is no harm in her work and her earnings are lawful.
Secondly, the fact that men and women are present under the same roof does not necessarily mean that there is prohibited intermixing between them, provided that the Shariah rules governing men-women interactions are observed, such as observing the Islamic hijaab, adhering to decency, avoiding being alone with a non-Mahram (marriageable kin), refraining from softening her voice when talking to non-Mahram men, abstaining from touching or shaking hands with non-Mahram men, and lowering the gaze from whatever Allah has deemed prohibited to gaze upon. The prohibited intermixing between men and women is when the due Islamic etiquette and Shariah rules are neglected. It is impermissible for the Muslim woman to work in places where she mixes with men in a prohibited manner.
Thirdly, the earnings of the woman obtained through her permissible work are lawful and there is no harm in availing herself of such money. Even if we assumed that there is prohibited intermixing between men and women in the workplace, she bears a sin for it but it does not affect the lawfulness of her earnings that she obtains in return for carrying out her lawful work (given the rule of infikaak al-Jihah which means the absence of any relation between two rulings, i.e. the prohibition of committing violations of Shariah in the workplace, on the one hand, and the lawfulness of the money received for the lawful work, on the other). What is forbidden is not the lawful work; rather, it is the indecent exposure of her beauty and committing violations of Shariah, whether in the workplace or elsewhere. Hence, the salary which she earns in return for the lawful work that she does is lawful, and the sinner bears the sin of what he commits.
Fourthly, there is no harm on you in benefiting from what your sister gives you from her money earned through her lawful work to invest it in trade or otherwise, even if there is prohibited intermixing between men and women in her workplace. The mere presence of such intermixing does not make her salary unlawful. Nevertheless, you should advise her to adhere to the Islamic teachings regarding her clothes, her going out, the way she speaks with non-Mahram men, etc. to the best of her ability; otherwise, she should look for another job where she would not have to mix with men in a prohibited manner.
Allah knows best.