I recommend you find yourself a holistic nutritionist. Don't forget, as someone has already pointed out ~ thirst is often disguised as a feeling of 'hunger'. Push more water ~ NO juices, and skim/low fat milk when it's mealtime. In addition... you do not mention if the fruits she is eating are 'raw', cooked, canned, etc.... The best way to have fruits and veggies are raw or steamed (just soft enough to tolerate.).
You also have to limit the fruit intake. Just because fruits are found in nature, it does not mean once ingested it will not turn to sugar. Most fruits are HIGH in sugar, so you have to be very, very careful of this trap ~ even dieters fall into this one thinking they are doing well, when they really are not.
Same with string cheese~ yes, it may have protein, but everything should come moderation.
You may have to become more strict about her overall diet. Set up a schedule of meals: breakfast, snack, lunch, snack, dinner and one last snack depend upon the time of dinner... My son does not get that last snack before bed. (Make sure the meals are healthy, watch the portion size, and be sure it contains veggies.)
Set this up where water is plentiful and outside the times set up for meals or snacks - there is no other food. Set up times, to get her body used to a time to eat, and when it should expect food.
Just like anyone getting used to eating correctly, that is what you want to establish, but also make sure you are choosing the correct foods - this is where a nutritionist can come in handy. Even though she is a baby, she does not require that much food all the time. You may also want to check in with a specialist to be sure there is nothing internally going on~ such as with the glands... (meaning she doesn't feel full).
At age 5, my son only goes into our refrigerator to fill his cup w/ water... or to assist me when I make his meal or dinner. He knows better than to just help himself. He can ask me and I will give him a choice of healthy snacks.