Hi, K. -
We have a 16-month-old daughter, and I can understand about getting rid of the "vice". We were giving our daughter a nighttime bottle when we put her down for the night, thinking that she was hungry, at least that's how it was when she was a few months old, so we just kept it going. However, we were TIRED of taking turns with getting up in the middle of the night to change her at least twice. Gradually, we gave her less formula, then just plain water. By the time she hit almost 13 months, we said no more bottle. That first week was tough, but we stayed consistent and just kept a united front with each other. She fussed and cried here and there, but eventually, she learned to just go without it. I'm really glad that we eliminated the nighttime bottle, and we've had pretty good nights of uninterrupted sleep.
As far as your situation goes, I'd just cut the binky off cold turkey - get rid of ALL binkies (cabinets, bedroom, the car, diaper bag, etc.) so that she can't see them anywhere. If doing it that way won't work, there's something that Supernanny did on one of her shows a while back....Explain to your daughter that she's a big girl now, and it's time to say good-bye to binky so that other babies can have it. Have a good-bye binky little "party", and put all binkies in a bag, and put it in the mailbox so the binky fairy can pick them up and share them with babies who need your daughter's help. As a reward for your daughter's cooperation, maybe give her a special dolly/bear/lovie of some sort (blanket might work, too). This way, she'll have something else to give her comfort, and you won't drive yourself crazy with the binky dangling in her mouth. All I know is that the earlier you eliminate something that your child really doesn't need (no matter if it's too hard for you or her), the better off you'll be, both short- and long-term afterwards.
Oh, and the screaming and crying when she's told no, just tune it out. I know it's not fun, but the more U hold your ground, the more she'll realize that it's not worth it for her to be overly dramatic about it. Our little one is ALREADY displaying the terrible 2's with her behavior here and there, and we tell her no. We explain why we tell her no, and if she continues with the tantrum, then what else can we do? I've been advised to scope out a "naughty spot" in all food stores, Walmart, malls, restaurants, etc., so that if/when our daughter misbehaves, the "naughty spot" is a universal understanding that bad behavior has consequences.
I hope this helps...I'm no expert or anything, just a Mom willing to go the distance for the sake of sanity!