Your packed lunch sounds great.
For context, my 12 year old makes his own sandwich for his packed lunch (eg fish paste and mustard/ salmon and mayo with cress/ egg mayo with cress) everyday. Once/week he chooses leftover Indian snacks and nan bread. These choices are always accompanied by a box of salad (lettuce , cucumber, tomato and radish). He takes a bottle of water. No crisps, sweets or sugary drinks: his choice.
NB He is autistic and likes the routine of have specific things on specific days. He chooses lots of fish because he likes it and knows that it promotes healthy brain development.
I guess he does get more carbs than your daughter because he generally chooses a sandwich rather than a wrap.
He goes to clubs at lunch and after school almost every day. Sometimes he eats lunch at breaktime so he has more time at his lunchtime club: his choice.
I expect him to be hungry by the time he gets home between 4 and 5pm and have the kettle boiled for a cuppa and a variety of heathy snack choices at the ready.
Usually he chooses tea with milk or plain Bovril with a small bowl of nuts/wasabi peas/chilli coated peanuts/japanese peanut crackers or a small sandwich (always containing protein). This doesn't mean that the lunch he chooses is inadequate. It is just that he is a growing boy and needs to eat often.
I would not get him a meal deal, nor would he want it. They are expensive and less healthy than what he chooses to make for himself.
I think that your plan of taking your DSD shopping so that she can choose is an excellent idea. Maybe she would like to make her own lunch as well, like my son does, so she is in control of her portion sizes.
Like all children, your DSD just needs to eat often and that includes a healthy snack when she gets home from a busy day at school. This is completely normal. Please do not be persuaded that her need for an afternoon snack indicates that her lunch is inadequate. This is quite wrong.
I wonder if her Mum is critical of your lunch because she is too lazy to ensure that her DD gets a decent homemade packed lunch and can't be bothered to provide her with a drink and a snack when she gets in from school.
Keep doing what you are doing. You got this.