Long road trips are not bad for cars.
Actually long road trips are great for cars as the engine gets up to operating temp and maintains that temperature for a long time.
That keeps the moisture out of the engine and the engine runs properly when it's at proper temperature.
Running a car just in town for stop and go driving does more harm to a car than driving the car on long road trips does.
Cars are meant to be driven and the more you drive it and the longer you drive the car the better off the engine will be.
When you drive your car on a long road trip you also prevent engine sludge buildup as well as long as you change the engine oil often enough as well as keep the oil level checked and the fluids all topped up the car should do good on a long road trip.