Kellie, this way of life is EXACTLY what will help your parents. Off fructose they will be off loads of foods that are a problem for diabetics. What I wouldn't do is start them eating lots of baking made with glucose and dextrose, that's just for birthdays and certainly will cause insulin to spike.
They will need to learn to love savoury foods. This is the most useful skill, but the great thing is some fat in the diet is better than having fructose, so a cheese scone with real butter for example is better than sweet biscuits, and even better if it is a wholemeal scone!
I had blood sugar problems, though not diabetes (yet) and now I'm so stable, I'm late 40's and was becoming frightened for my arterial and heart health, as well as needing to lose weight badly, and couldn't make any change more than for a few days at a time until I cut out sugar. It's like a fog has lifted! I'm slowly losing weight, with plateaux, and as David suggests, cutting back on carbs helps when that happens. I can feel genuine hunger and go longer without nibbling, and eat less at meals. My confidence in my body is growing , my trust that it knows what to do ...now. This is the most amazing thing of all.
I hope you can get your parents to read up on this, once through the difficult withdrawal phase.... which is do-able once you've read how bad fructose is for the health in every way. Also you should watch the hour and a half Youtube clip by Robert Lustig, an American Endocrinologist, just search for Bitter Truth Sugar on Youtube and you'll see it. He works with obese kids in the states, and is very knowledgeable, great to hear the same message in more detail ...with visuals, from someone else!