Filial piety didn’t require blind obedience to your parents – at least not the version of it that Confucius taught. In Chapter XVIII of Book 4, he says that you may “gently remonstrate” with your mother and father if you think that they are not conducting themselves in the right manner. He does go on to caution, however, that if they choose to ignore your advice, you should “remain respectful” and not let “your efforts turn to resentment.” In the final analysis, maintaining harmony within the family is more important than being right.
In Book 4, Confucius also tells you to treasure your time with your parents by reminding you to always keep their age “in mind” and to let this knowledge be “a source of joy and dread.” In addition, he advises you not to travel far or at least stick to a fixed itinerary while your parents are alive, presumably so that you can be easily reached if they happen to fall ill while you are away.
Confucius concludes by warning that your obligations towards them don’t come to an end when they finally pass away, noting in Chapter XX that “If for three years after his death the son does not alter his father’s ways, he is a good son indeed.”
Three years was the traditional period of mourning following the death of a father, though it was probably honored more in breach than practice given the stringent demands it placed on a newly-bereaved son. You can read more about it here.