Should one continue to help others with his car despite his wife's objections and the increased burdens, or should he refuse their requests? Is there a middle ground that satisfies all parties and achieves reward and Allah's pleasure?

Helping people is one of the greatest acts of righteousness and good. There is encouragement to strive to fulfill their needs, for a Muslim is the brother of a Muslim, and Allah helps His servant as long as the servant helps his brother. Therefore, if you can continue the good deeds you practice without hardship that exceeds your capacity, then persist in them and try to appease your wife by explaining their benefits. However, if you find excessive difficulty, there is no harm in excusing yourself to those who are not in dire need, for Allah does not burden a soul beyond its capacity.