Sorry OFL, I was mearly implying that it may not be a personality disorder and something that can be easily remedied if the child is taught boundaries. I would first look into if there is something that can be fixed. As someone else just mentioned, pets are not disposable...
If however you find that the child is not instigating the agression, and the dog cannot be trained, THEN should you rehome it.
However its hard to understand what is meant by "now my dog has started snapping at my youngest son", I may be taking it lighter than it actually is. A large dog + small child? I just don't know all the details.