You may find the threads entitled ‘Has the Link Between the Gut & the Skin Been Investigated?’ (Newbies forum) and ‘Long Term Lymecycline Use for Acne’ (Welcome forum) useful.
There are different forms of rosacea with different underlying causes; triggers and severity vary from person to person. What all sucessful treatments have in common is reducing underlying irritation/ inflammation. Diet and lifestyle are highly relevant here.
The first step for your wife is the detailed food and symptom diary (p.187 + p.266-267). Consider potential trigger foods, drinks or situations (see lists on the National Rosacea Society website), intake of pro inflammatory foods (sugars, refined or processed carbs, omega-6 rich fats) and anti inflammatory foods (oily fish, brightly coloured low sugar fruits & non starchy veggies, some seeds).
Any supplement regime should be tailored to the individual, considering their medical history, diet and lifestyle choices. This means consulting the family doctor, a registered dietician, dermatologist or pharmacist.