From `bash` documentation, [Brace Expansion][2] section:

> **Brace expansion is performed before any other expansions, and any
> characters special to other expansions are preserved in the result**. It
> is strictly textual. Bash does not apply any syntactic interpretation
> to the context of the expansion or the text between the braces. To
> avoid conflicts with parameter expansion, the string ‘${’ is not
> considered eligible for brace expansion.

Another note, in `bash`:

> The order of expansions is: brace expansion, tilde expansion,
> parameter, variable, and arithmetic expansion and command substitution
> **(done in a left-to-right fashion)**, word splitting, and filename
> expansion.

So in your case, `bash` *saw* brace expansion before variable expansion, it will do brace expansion first, produce result `{Alpha,Bravo,Charlie}`.

If you can control `$find_dir` variable content, you can use `eval`:

    eval "find Directory/{$find_dir} arg1 arg2"


  [1]: http://www.gnu.org/software/bash/manual/html_node/Shell-Expansions.html#Shell-Expansions
  [2]: http://www.gnu.org/software/bash/manual/bashref.html#Brace-Expansion