Now that you mention it, I've wondered if there is a deep, dark secret in the Anthony family. Attempts to keep the world from finding out what it is could possibly explain some of their bizarre behavior. My only problem with that theory is that I just can't come up with anything that would be so secret and so horrible that they would be willing to let their daughter get away with anything, even murder, in order to keep it covered up. Maybe I just don't have a vivid enough imagination?
The donations angle is still what makes the most sense to me... although I'm not sure if they would have been thinking about that from the very beginning, would they? So maybe it doesn't explain their weird behavior early on, I don't know.