I confess that I find it hard to imagine Nicholas whipping his daughters hard until they were screaming, it sounds so unlike him. I don't think the children were necessarily very afraid of their father, as all of them (except Tatiana) were closer to him than to their mother and considered him a friend as well as a father. However, they did respect him very much, and it is said that he was the only one that Anastasia and Alexei, at least, obeyed. I guess that sometimes "respect" for a parent does contain a little bit of fear (fear of punishments) for children, so in that sense they may have feared him when they were little.