Firstly its not the right time for the East Coast Tour ( Again not sure when you are planning ). I wouldn't plan until end of May if you want to have a pleasant outdoor experience.Secondly togo bus keep you rushing between the places.By the time you start to enjoy the place you'll be rushed to other place. I wouldn't plan my trip, I don't like someone pushing me on time constraint.
Unless you don't have enough time to accompany your parents or you want to skip the driving and if you are looking for a feel that you covered BLAH BLAH BLAH places during your parents visit, I wouldn't go for goto bus.
My thinking is though you cover 2 places, make sure you guys enjoy every sec.