My DD is similar, same growth lines etc. Typical day for her:
Breakfast - half portion of fortified porridge, or a slice of toast & butter and a piece of fruit and a drink of milk.
Lunch - sandwich with protein, occasionally a few chips if we're out for lunch, some tomatoes etc & maybe some fruit.
Dinner - hot meal if lunch was cold & vice versa, so: 1 large slice toast & scrambled egg, or fish pie with broccoli, sausage & mash & peas, perhaps a sandwich, pasta bake etc.
Bedtime drink - about 200 to 250ml semi-skimmed milk.
All meals include protein in some form - even if only as a drink of milk or a piece of cheese on the side, or a boiled egg. Also, some fibre foods, like tomatoes, cucumber, broccoli, peas, baked beans, fruit etc. It keeps her full for longer.
She rarely snacks at home (rarely asks) even though they do at nursery. If she does, it would be a piece of fruit or a breadstick. She is a total livewire & constantly running around, not visibly overweight. She does have smoothies & juice occasionally, generally before or with a meal.
Sounds simple but is she drinking enough? Apparently hunger and thirst can be easily confused. And if possible, don't offer sugary drinks on their own as they will raise, then drop, her blood sugar, which causes hunger.
Yes to distraction - if she's hungry try playing a game or something. She won't expire if she doesn't eat for half an hour. If she's still complaining of hunger after that, and has had a drink, then get her something.
If you think she's asking for unhealthy foods a lot - offer only plain, healthy ones. Not crisps/chocolate/grapes. Grapes are ok in moderation, as part of a larger meall but very sugary on their own.