you should just add your own connection string in user.config or web.config and read it from there, you should not add a separate web.config file in your feature folder.
ie we have this one for mojoPortal:
<add key="MSSQLConnectionString" value="server=localhost;UID=mojouser;PWD=mojo123;database=mojo" />
but nothing stops you from adding your own for your separate db:
<add key="MyFeatureConnectionString" value="server=localhost;UID=youruser;PWD=yourpassword;database=yourdb" />
public static string GetMyFeatureConnectionString()
{
return ConfigurationManager.AppSettings["MyFeatureConnectionString"];
}