Diabetic ketoacidosis is MUCH more common in type I diabetes. If you were to develop diabetes it would most likely be type II. Diabetic ketoacidosis is the most common cause of "diabetic coma". While type II diabetics can technically go into something called hyperosmolar coma, I have seen diabetics push 1000 on their blood sugars without any serious instability of vitals.
Normally I am here for moral support and to tell people their fears are in their head. While I believe your fear of coma from diabetes is catastrophic thinking, your fear of diabetes is not. With a family history and some weight issues you have a strong likelihood of becoming diabetic at some point. What is good about this is type II diabetes many times can be avoided through simple lifestyle changes. These would not only decrease your liklihood of diabetes but would help your anxiety. You are likely in a vicious cycle of emotional eating, which adds weight, which worsens self esteem and increases cortisol and other stress hormones. I would start your treatment for anxiety not just with cognitive behavioral therapy but walks in the park, and weight lifting. The best way to burn fat and decrease glucose levels is weight lifting...for men and women. Women overlook weightlifting but it's hands down the BEST type of exercise to decrease fat and it's not even close. This would also greatly help with anxiety, depression and insomnia. If you are like most women who are a few pounds overweight you probably feel self conscious going to a gym. So, start light at home with some dumbbells, add ankle weights to your walks, if you have room in your home for a small weight room with a squat rack there is nothing better. Couple this with strict calorie counting (dont get sucked into carbs vs fat debate it's all nonsense), eat frequent small meals 5-6 times a day, lots of water and stay under 1800 calories. You will watch a slow and steady decline in weight, and a great improvement in your anxiety and depression.
PS-before you start any diet or exercise program talk to your doc to make sure you are fit enough to handle it. Not to mention it would be a good idea to get your BS checked.