Is the statement of the questioner's sister-in-law that there is no partnership in Islam between a man and his wife, and that the names of wives in a company do not mean they have a right to it, correct?

What your sister-in-law said has no basis in Islamic law. There is no impediment to a wife being a partner with her husband in business, nor for a sister, mother, or daughter. The fundamental principle in dealings is permissibility, and the fundamental principle regarding partners is generality. Whoever prohibits something must provide proof. Whether he includes her in the partnership with money she contributes alongside him, or he gifts her a portion of the company's shares, there is no objection to that.