My guy just turned 4, he finished the last of his Halloween candy a couple of weeks ago, the suckers. His Easter basket only had a few candies, the rest was crayons, bubbles, stickers, etc., the same with his Christmas stocking. He has no cavities, the dentist said his mouth is as near perfect as it can be, I know that won't always be the case but want to aim for it. He doesn't get candy every day, even if he eats all his healthy foods. I limit it. When he brings it home I go through it, put it out of his sight and reach. If he sobbed for not getting some I'd send him to his room, discipline the tantrum. If he threatened me I'd probably ditch whatever candy we had to show him he doesn't threaten me.
I'd just limit the candy she gets, one piece every few days. Toss or give away most of it, I put some in a bowl on a counter he can't see or reach and others eat it. Remember, candy is a treat, not a major food group. You're the mom, you call the shots. Introduce her to healthier treat options, other than straight sugar. My guy loves sweet potato fries and mashed sweet potatoes.
Yes, kids like candy, but it doesn't mean they can have it whenever they want. We have to be the voice of reason, don't try to explain it to her, she doesn't or want to understand. But just because she asks for more doesn't mean you have to give her more, use your control while you can because when she's older you won't always know, she'll eat it away from home. If you can curb her taste for it now she may not go crazy over it later.