The Elm at the Edge of the Earth by Robert D. Hale

It has been a few years since I read this book so I actually had to read a synopsis to remember the details. But what I do remember is what a great story it is and how often, even years later, scenes from it will pop into my head and make me wonder.
David is a young boy who is sent to a country institution while his mother is seriously ill. There he makes friends with the inmates, each a little stranger than the last. But his best friend is Rose, a woman convicted of killing her husband with a butcher knife. Throughout his stay David and the reader, learn from his friends about the intricacies of life through humor and heartbreak.
You may have some trouble finding the book, because it's no longer in print and a lot of libraries don't have it (Amazon does have some copies for sale). However, it is worth whatever searching you have to do.