The Halocho rules that, on chol hamoed, one may only do melochos (creative labors) which are needed for the Yom Tov. What justifies doing melochos when going on family trips? Surely these trips can be done after Yom Tov!
Sh'miras Shabas K'hilchasah, chapter 66, paragraph 58 and footnote 224, discusses riding in a car on a pleasure trip on chol hamoed, as follows. Rav Sh'lomo Zalman Auerbach suggests that it may be permissible even if one can walk, because the m'lacha involved in riding in a car is hav'ara, burning [gasoline], which is permitted on chol hamoed; but he's unsure, as operating the car may be considered m'leches uman, skilled labor, which would be forbidden. Rav Moshe Feinstein suggests that driving is more pleasurable than walking for most people, so that — SSK adds — as long as the trip is for some pleasure for chol hamoed (e.g. visiting a friend), it's permissible as tzorech hamoed, needed for the holiday.