I think the general rule is that when you're talking about specific things or people, you use "between" and when you're talking about a general group of people/things you use "among."
"Let's keep this story a secret, just between you and me."
It would be incorrect to use "among" here.
"Peace has spread among the people."
"Peace has spread between the settlers and the natives."
"She lay among the flowers"
"She lay between the daisy patch and the lilies."
"between" is also a more accurate indicator of the physical location than "among."
Hope others can provide a better answer.