Is a wife's intention to buy a new dress for a wedding party to avoid people's criticism considered shirk (polytheism), and what should the husband do in this situation?

A wife's fear of what people say is not shirk (polytheism). It is viewed through the lens of extravagance and wastefulness, or generosity and frugality. Improving one's appearance is religiously مطلوب (desirable/required) and naturally محبوب (liked/loved), but it should not reach the point of extravagance. Spend without extravagance or frugality. If buying clothes is affordable, there is no harm, as the Prophet, peace and blessings be upon him, said: "The best among you is the one who is best to his family." However, if it involves تكلف (undue burden/affectation), then it is forbidden.