Hi - I have a wide range of experiences in communications, marketing and business development in both manufacturing as well as 'premium' markets. While coffee is not considered a luxury per se, good coffee should be promoted as a premium experience - especially Turkish coffee which is not widely available and not very well understood. (I myself am a big fan).
There is a lot of work to be done to accomplish your objectives, but I could provide you with the core elements to take the next steps, including a new brand identity, logo, packaging, as well as a communications plan for the media and your web and social media presence. You can then decide to continue to execute the plans going forward on your own, or we can negotiate an ongoing collaboration going forward.
You have a significant challenge ahead of you. While Turkish coffee is not widely known or available at coffee shops it is available in all supermarkets. Depending on your price point (I expect you are more expensive considering your operational size) the positioning would have to be a premium one, telling your story, your family's as well as the story of good Turkish coffee and why it should be your product people prefer.
To make you a final proposal I would need to discuss this in a little more detail.