It is a common myth that poor diet will cause someone to develop diabetes. This is totally wrong. It is more likely that one is predisposed to a failing blood sugar regulation, with environmental factor as well.
There is an excellent article in Blood Sugar 101 where the author discusses this subject
You Did NOT Eat Your Way to Diabetes: The REAL Causes There’s a full discussion that begins with how overweight people are told it is their fault, but if you can wade through this lengthy article, you’ll find the discussion of what actually DOES cause diabetes.
This quote is just one of many very important bits of understanding about diabetes that addresses the heredity component.
When these genes are damaged, they keep your body from being able to regulate your blood sugar. If you don't have these damaged genes, you can eat until you drop, pack on hundreds of pounds, and never develop diabetes.
Knowing the true causes, and understanding the role carbohydrates play in raising a person's blood sugar, should give you the tools to keep careful watch on your own body's blood sugar management, and to take steps to minimize rise in blood sugar should it begin to occur. While one can't cure diabetes, one can certainly manage it and maintain near normal blood sugar levels so that one doesn't have to develop diabetic complications.
You are in a good position right now to make sure you don't follow the course of your relatives. Just a periodic checking of blood sugars with a meter, as hftmrock suggested, should be all you need to do. I'd add, though, that testing 1hour after a meal, especially one with plenty of carbs, would give you an early warning to start watching more closely and take seriously reducing carbohydrates in your diet.