Is it permissible to sign a commercial partnership contract in the wife's name and a debt contract in the husband's name to protect the money, due to the law prohibiting lawyers from practicing medicine and trade?

One must adhere to laws that serve the public interest and do not contradict Islamic Sharia (definition). Authorities have the right to enact laws that regulate transactions to achieve benefits and avoid harms, keeping in mind that the original ruling is the permissibility of trade, as Allah says, "And Allah has permitted trade and forbidden interest." If a law achieves an overriding benefit, then adherence to it is obligatory. If it does not, then there is no impediment to circumventing it through a permissible stratagem. However, drawing up a debt contract with one's wife or partner as a stratagem is not permissible, because a partner's money is a trust, not a debt.