Well Dr.Atkins specialized in cardiology. He was convinced that there is nothing wrong with eating fat and that sugar and starches are really the problem in our diet. So we who follow his plan we eat our fats with good conscience.
On the Atkins plan - which is a ketogenic diet (and least for the first part) - fat is necessary to achieve that.
There are low carb plans out there that emphasize lower fat - (such as protein power or South Beach) but if you chose to follow one of those you should find out what they think you should eat and follow that.
Have you looked at the list of allowed vegetables - there are about 40 there. Have you even tried all of them (I know I havent) Don't cut yourself short. Vegetables are super important - start trying them again. Find new ways to prepare them. Some people over cook everything so they do not even know how vegetables really taste like.
Check out this page for recipes:
Linda's Low Carb Menus & Recipes - Home