I'll give you my best advice. First, only ONE cup of juice a day, and it should be watered 50/50. Two or three cups of juice a day is too much.
If you are brushing her teeth AFTER breakfast or dinner, and she has had juice, that's even worse...basically, you rub the acid/sugar into the teeth and can cause further damage. Wait at least 30 minutes before brushing, or brush before breakfast (I know this seems silly, but that's what we do, and no cavities yet. My oldest is six.)
You don't have to limit all treats...especially not cake, or sugar free gum. There are a TON of yummy sugar-free flavors...I forget who makes the Dessert Sensations gum (it's new) but they have a mint ice cream flavor that is so yummy and it's sugar free! Also, there are fruity sugar free flavors. Nothing wrong with gum, if it's sugar free.
However, your dentist is right about the gummy snacks, candy (both hard and chewy) and ESPECIALLY dried fruit...it has a TON of sugar, the fruit is super concentrated and super sticky, and that stuff just sits on your teeth. Dehydrated fruit is junk food...not lecturing you, either, because I just polished off almost a whole contained of dried mango slices today! Yum! Ditto on the juice, pop, mints, etc...don't give them to her, unless the juice is watered down and then only a total of about 4 oz a day.
Hawaiian Punch makes an awesome sugar-free water flavoring. You can buy a box with 8 or 10 little packets for a dollar. A DOLLAR! :) Each one will flavor a 32 oz bottle (like, a Gatorade bottle...I buy one, and reuse it about 100 times) if you don't fill it quite up, and it's very yummy. They have all kinds of flavors.
Yes, these teeth will fall out, but likely the teeth she has coming in are going to be just as prone to cavities. However, if you get it under control now (especially the juice and sticky/hard candy, those are the worst) you can set her up for beautiful teeth.
One thing to remember is that the enamel on her baby teeth was probably worn away from going to bed with a sippy, so that's mostly why she has so many cavities now. I only say this because it can be a positive thing...now that you know, you can set her adult teeth up for success.
So many of my friends have children with these problems with their teeth, and they all have the same contributing factors. So I know you can do it from here!
(I'll also add that I didn't take care of my own teeth as a teen/young adult, and I have a mouth full of gold caps. I am so thankful that my front teeth are still white, but I am very good at scaring children into good dental habits by opening wide and showing them all the gold in my mouth. Except those who think it's cool. You can't win 'em all.)
Good luck...you can do it! Good for you for making the changes, and who cares what the dentist thinks...don't let her get you down. Maybe look for a new one. :)