How do I deal with my wife and brothers who support a political party with which I disagree, especially given the differing opinions among scholars regarding the legitimacy of this party?

The basic principle is that your brothers and wife should not support an oppressor or a transgressor. The fact that they do support him might be because they have a good opinion of him and a bad opinion of his opponents. Therefore, they are more in need of gentle and kind advice, not enmity. You should consider their situation: if they love religion and goodness, then find excuses for them. It is sufficient from them that they affirm the fundamental Islamic principles, such as the sovereignty of Sharia, the prohibition of injustice, and the glorification of the sanctity of Muslims.