My wife has developed rosatia on her face and has been recommended to stop eating dairy. Is there really a correlation between these two things?

Dairy is not.... ..A common rosacea trigger. They are (in order of frequency) sunlight, stress, hot weather, alcohol, spicy foods, exercise, hot baths, and hot drinks. However, dairy products do contain hormones which may trigger rosacea in rare cases. Each case of rosacea is different, with different triggers; you can determine your wife's triggers by noting what she ate (or did) right before she has an episode.
Often a correlation. Even the most conventional doctors now recognize that rosacea is often aggravated by a wide variety of foods, especially spicy foods, acidic foods, hot drinks and alcohol. For many people dairy also aggravates it. The only way to know for sure is to try avoiding common triggers for a few weeks and then add them back individually to see how they affect her. Please see comment for links to more info:.