It's not the fat content in your diet that gave you diabetes; it's the high glycemic carbs. High glycemic carbs or too much of even the good kinds of carbs can cause havoc on a diabetic's blood sugars.
Diets that are high in fat and low in carbohydrates also have never been shown to contribute to or cause heart disease in any way. All of the studies that they say shows fat gives you heart disease are also high in carbs and sugars.
You may want to do a bit of reading through the cholesterol/heart disease forum for more information on the topic or you can also visit this website: www.thincs.org for some very interesting research on the whole idea that healthy dietary fats (not the trans fats or hydrogented fats) cause heart disease.

I very much agree with Jim's suggestion that you get and read Dr. Bernstein's Diabetes Solution Diet. Even if you don't follow the plan, it's excellent information to know and have on hand to refer to.