Do you use whole grain bread or whole grain pasta? Are you making pizza, chicken nuggets or mac & cheese from scratch or is a pre-made item?
The limited menu isn't exactly unhealthy if you tweak it. I would start with getting your dd to eat whole grain versions of bread or pasta and healthier homemade versions of her favorites.
You could try a sandwich with peanut butter and slices of fresh fruit like strawberries or banana instead of jelly.
I would skip hot dogs except for very rare occasions.
Would your dd eat chunks of cooked chicken or turkey instead of a breaded nugget?
I would just keep offering new things at home. My dd was wary of new foods but accepted a shift to whole grains pretty easily. www.webmd.com/food-recipes/features/15-fre