Nancy -- I'm exactly the same way. I always thought there was something weird about me, but if I read a book that has something difficult at the beginning -- especially if it has something to do with a child being hurt -- I can't read the rest of the book. I give it away.
The only time I was able to read a book that had a gruesome first chapter, was a non-fiction (true crime) journalistic book about the Son of Sam killings. It's by Maury Terry and it's called Ultimate Evil. The first chapter is meant to catch your attention, but it is difficult to read. The rest of the book is a fascinating story about the Son of Sam and his ties to the Satanic cults in this country. It is amazing all the people who tie in to this cult and how Berkowitz, Manson, and some other famous people, were connected to this cult. In fact, Maury Terry makes a very good case for there actually being FOUR killers. They are all dead, however. Berkowitz is the only one of the four killers living but he has never revealed this information publicly.