Have you spoken with your pediatrician about your "tummy poke" method? That isn't a proper way to gauge whether your child is full...at that age, they don't eat for emotion or any other reason. If she wants more food, it's because she is HUNGRY.
There is no "correct" amount at this age. Feed her appropriate portions of healthy foods. Do a little research on what a toddler sized portion should be, and you would be surprised. For example, the folllowing are each ONE serving of a food for her age...
1/2 cup yogurt
2/3 to 1 oz. cheese
a whole egg
1 oz. meat
1/4 cup peas or beans
2/3 c. fruit
3 Tbsp. vegetable (proper, not talking about white potatoes)
1/3 slice whole grain bread
1/2 oz. ready to eat cereal
1. tsp oil, mayo, margarine, butter
Now, they need 3 servings of dairy, 2 servings of meat/protein, 4-5 servings of fruits/veggies, 6 servings of breads/cereals, and 3 servings of fat/oils. So an entire SLICE of bread only takes care of 2 out of 6 servings...so let's work this out.
Breakfast...cereal with one serving of milk, 4. oz of juice mixed with water, and a banana.
Lunch...an entire tuna sandwich, some whole grain crackers, strawberry slices, an 8. oz glass of milk
Dinner...some sort of casserole with meat, veggie, and cheese, a slice of bread with butter, another 8 oz. glass of milk...
And you still haven't met your daily requirement, so you could supplement with healthy snacks.
Sounds like a lot for a little one, doesn't it? The key is some days they'll eat all that, and some days they won't touch a thing.
My biggest concern here is that your daughter is "underweight" (which is why her tummy feels hard when she eats, or because she's constipated, but it's NOT because you feed her too much) and you want to put her on a diet!!!! Babies are NOT to be on diets!!!