Hello Smof1. I totally feel your pain. i just went through this in February! It's hard, but I took my son's pacifier away - just cold turkey. When he would get to the point where he would start looking for it, we would just distract him with a toy or a cup of water or something like that. That worked fine, but... the worst part was naps/bedtime. He was sooooo dependent on it, but especially worse at those times. The first night was torture. I put him in his bed and he cried and cried and I picked him up and soothed him, then put him back down. I did the same thing over and over again about 6 times, then I just pulled a chair up to the crib, put him down and slid my arm through the slats and rubbed his back. Eventually he went to sleep. By the third day he was fine, but all babies are different. The problem I have now is that I can't get him to sleep without nursing him, or putting him in his crib and turning Veggie Tales on for him, which he'll watch until he falls asleep on his own. On the other hand, my daughter can get him to sleep by rocking him, but I can't because he'll twist and turn and get under my shirt for 'boobies'. The funniest thing is, the other day he found an old pacifier (I thought I got rid of all of them) under the bed. I watched him to see what he was going to do, and he picked it up, looked at it kind of funny, then threw it on the ground and went about his business! I was soooo glad he didn't try to suck on it. I say, forget about cutting it or whatever, just get rid of it. As far as your parents go, that's a different story. I don't know how often your daughter is with them, but if it's during the week, try getting rid of the binky on a Friday night, that way you'll have the whole weekend to deal with her by yourself, and then when she goes to see them, she should be at a better point. Best of luck to you on this, I know how hard it can be. And believe me, the first night, I was ready to pull my hair out and run away, but now I am so glad that I did it. We used to look for the binky before we did anything. It was always "Do you have his binky?" before ANYTHING!!! lol Now we don't even have to worry about it, because it's gone.
**ok, so I just re-read your post. sorry I missed it the first time, when you said she is with your parents twice a week. Get rid of it the last time she sees them for the longest time before she sees them again. she should be adjusted, or on her way to being adjusted to it, by that point. If she has any pacifiers at their house ask them to please get rid of them, and do NOT, under any circumstances, give one to her, because all of your hard work with be for nothing. If they don't have any at their house, then just don't bring one for her when she goes. they'll be forced to deal with the situation. again, best of luck!!!