I would skip the "refined sugar treat" for the 100 calories that the sugar treat gives she could have a pudding or jello. Instead of apple maybe apple sauce in the little travel size cups or
exchange apple for 1/2 banana. If apple is only choice --add a bit of peanut butter as a dip for apple.
I would use whole grain bread of some kind instaed of the pita. Make sure the meat you are using is not filled with added fats for taste. ( We seem to love the taste of fats like butter). Pile sandwish with lettuce or any vegetables that would not make the bread soggy and daughter likes. What sandwich spread are you using? What is she drinking at lunch? Milk is best but some juices are very filling also. carrots with ranch dip. or small carrots with olive stuck to the end of each. ( fun for small kids to eat). depending on age maybe a snack between lunch and school release time.
I totally agree make a high proten breakfast with some complex carbs. that should keep her full till lunch or longer making her start out ahead of the game at lunch.
Bless you for helping your daughter.
I have a hard time realizing there are kids hungery everyday when they go to school due to no dinner night before.

I then hate to see kids eatting chips, candy, pop as drink and if sandwich it is not even touched at lunch time.
Side note If you do up her proteins please make sure she gets plenty of water --

Hope I help -- with some "FOOD FOR THOUGHT"