sorry to tell you but basically what the others said. 4-6 oz(which is less than a cup) daily. yes, juice could substitute for food, but aside from that, juice is the number one cause for cavities in young children. juice also is adding calories to her diet which isnt setting up good habits for later in life. juice, even though i would say is better than soda, still is complete sugar, and too much sugar in the diet affects her activity level, and diabetes concerns later in life. my doctor while pregnant actually told me not to drink more than one glass a day as well.
of course, no one is saying she is going to be ruined for having a lot of juice, but if you are asking if its good to drink alot, the answer is no.
i know its hard, but just let her cry. what we have been doing with tantrums is telling our daughter if she is going to cry, she needs to go to her room and do it there. we bring her in there and she screams by herself until the tantrum is over, then comes out. you are in control, and you want to make sure she doesnt think crying will get her what she wants. i would agree with the other saying just dont buy the drinks. also, try and only get the "real juice with no added sugar". its more expensive, but def more healthy. and then only give her 2 oz with like 4 oz of water. actually it would be better to put like 1/3 of a pitcher, then fill the rest with water and put it in the fridge. that way, it will be quicker, she wont actually see you water it down, and you will be more consistent on how water down it is so it will always taste exactly the same to her. that way she can have 3 cups a day. she may be all upset knowing its watered down but in a week or 2 she wont even care. just tell her its that or nothing, put it on the table and walk away. if you stick to your ground, and only give her the water down 3 times a day, she will eventually know thats just how it is.
aside from that, i would really encourage you to give her more milk and water. if she has no allergy problems with it, give her soymilk, and again, she may not like it at first, but will get used to it. also water is really important to get a child to like it to set up good habits for the future.
my daughter is 3 1/2 and has had juice about 5 times. her teeth are perfect, and she asks for organic milk only, and i also give her water. i know if she had juice, she would want it all the time. i also think if i ever let her have chocolate milk, she would only want that as well. the easiest thing to do is to never give it to her, and then she doesnt know it exists. otherwise if she has something sweet one time, she refuses all else.
good luck, im sure you can do it:) just remember, she will adjust, they always do!