First, I'm sorry for your loss of a baby, that is so very hard to deal with. BUT, your first concern is for your little girl.
At age 2 she should not be allowed to control you -- you are the one who controls the food availability, so the statement that all she will eat is junk and snacks tells me that you're giving in to her typical toddler whims. It's normal that they choose that over the "yukky stuff". LOL
The solution is very simple, if you don't eat junk don't give it to her either. IF you are eating junk, stop having it in the house and change your own habits to a more healthy eating plan. Don't buy it, don't keep it, don't give it to your daughter. There are so many good snacks and finger foods out there with many options for healthy eating, it makes no sense to continue feeding her food that you know, especially as a diabetic, is not good for her.
Children will NOT starve themselves, and when you as the parent take control, she will eventually come around. In the meantime, start making mealtime or snack time a stress free and fun event. Perhaps you could buy to veggie seeds and have her help plant them in a pot, help maintain them and when ripe, pick them and have her help you prepare them for eating. Kid usually love to do that, and since they had a role in "creating it", they are more likely to eat it. I made "party plates" with things like wheat crackers, cheese, apple slices, or a small pancake with cut up fruit on it in the shape of a smiley face. String cheese, yogurt, applesauce, carrot sticks, are other examples of snack type foods or even give them as part of the meal.
Another snack most kids love is dry cereal, such a honey nut cheerios, or rice chex. Be a little creative and make it a special thing, and let her "help" with fixing the food.
Offer her healthy alternatives, is she refuses to eat it, put it away until she asks for food again, then give her the same snack. She will eat at meals also if you focus on family mealtime and not on giving her junk in between that steals her appetite or willingness to try new foods.
I agree with others that if you don't get a handle on this now, it'll be much more difficult later on. Remember, you're the parent, and the responsibility of what is available for her to eat is yours. If DH objects, that's another issue, but you all should basically be eating the same healthy foods.