Why does dew accumlate on only one side of my car?
The formation of dew is due to atmospheric moisture and temperature.

Given that dew forms on all sides of your car at your mother's house, this makes me think the car is more exposed at you mother's house so that the car is uniformly cold and the temperature of the car is at, or below, the dew point.

With dew only forming on one side of the car when at your father's house, this tends to infer there is a temperature difference between each side of the car; with the side of the car on which due forms being colder.

You mention that dew does not form on the side of the car facing a tree. If the tree is sufficiently large and leafy (bushy) and the car is close enough to the tree, the tree can shield the car from the cold air thus making that side of the car slightly warmer than the other side of the car. As long as the temperature is above the dew point, due will not form.

Dew point varies for atmospheric moisture content, temperature and air pressure.