As others suggested, and regardless of the extra time it adds, I'd schedule fairly frequent stops, at least one every 2-3 hours -- to monitor your daughter's blood sugar, give everyone a chance to stretch their legs, etc. (My mother was also a Type 1 diabetic, so my entire childhood was built around frequent potty breaks!)
As for keeping the kids amused in the car, we recently spent a solid week on a family road trip in which we traveled 2-8 hours every day. In addition to a portable DVD player, we had good success with surprise "care packages" for each child -- each with a kid-sized neck pillow and lap blanket, an inexpensive lap desk, a binder of coloring pages and games (no need to buy them - there are TONS of free printables online with coloring pages, games like the "license plate" spotting game and road trip bingo, etc.), which also contained fresh scratch paper, a map of our road trip (so the kids could mark off various milestones as we passed), and a binder pouch of washable markers and erasable colored pencils. (We didn't take crayons, as we were traveling in the South in summer, and didn't want them to melt.) We also passed out healthy snacks periodically -- in keeping with your daughter's condition, I assume you'll want low-carb options (e.g., mozzarella sticks, celery sticks with ranch dressing, sugar-free fruit gummies, nuts, hard-boiled eggs, etc.).
When it comes to the parks -- the advice is the same. Plan your day to incorporate plenty of breaks. Growing up, our practice was to stop and use the restroom every time we passed one (even if we didn't think we had to go) -- that way, none of us every "suddenly" had to use the bathroom in the middle of an attraction queue, and my Mom got to test her blood frequently. Although my Mom is no longer with us, we still tour the parks that way.