What is the ruling on a husband paying off his wife's debt from his own money, then her partnering with him in a business from which she takes the profits as spending money, while refusing to be held accountable, which prompted the husband to take a portion of the invested capital to compensate for what he paid and for the profits he did not receive?

Firstly, if you paid off your wife's debt from your own money as a donation, you do not have the right to claim it back or demand its equivalent from her money without her knowledge.

Secondly, for a partnership to be valid, the profit-sharing ratio must be agreed upon. If the ratio is not specified, the partnership is invalid. However, if it is specified and you forgo your share of the profit, there is no objection. It is permissible for you to give her money for investment, with all profits belonging to her; this would be considered a loan to her. It is not permissible to enter into an invalid partnership, nor to take money from the partnership – whether valid or invalid – without her knowledge.