Rowling has said in interviews that Harry's parents are dead - that he was too young, at 15 months, to realize what was going on, so he couldn't see the thestrals. It's also why he didn't see the thestrals on the way home last year - it took a while to sink in.
Unfortunately, James and Lily and now Sirius are really dead. She has an unpleasant habit of killing off characters I like.
She also said in an interview that she isn't writing this stuff to make people's children feel safe.
It's quite clear that she has had the whole story outlined from before the first book was published, and will not alter anything to make it more pleasing.