Having both parents with diabetes, your risk of developing diabetes in your lifetime is as high as 50%. Doing yoga or other forms of exercise certainly help, but sometimes genetics are stronger than the benefits of exercise and diet. Regular monitoring is recommended.

Any type of exercise with a good diet can prevent diabetes. The key is not gaining weight and being able to follow this long term

Yes it can but not always. Type 2 diabetes is a genetic disease and with both parents having the disease (I presume they have Type 2), you are at very high risk. The mental aspects of Yoga will help your mental & spiritual development but will not prevent diabetes. Even though diabetes is a genetic disease, there are environmental factors mainly weight. So keep your weight down, eat right and exercise. Yoga will help with the exercise part. Good luck.