From `bash` documentation, Brace Expansion 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"