Usually people pick up small cakes at your house. Some decorators I know deliver even these. Mostly because their home is not located in a business ZONE and this is the only way to maintain a business from their home. But, with wedding cakes, MOST are delivered. There are things we can do to make certain the cake gets to the party location in good condition.
Some cars ride smoother than others.
Obviously the smooth-riding car will do best. If you must use a more rough-riding car, then you should drive more slowly. Cakes can be either place in a car's trunk or in the back of a van. For short distances I had no problems with icing melting, etc. Never place a cake on the car seat.