I understand the bottle attachment thing. My 16 month son was VERY attached to his bottle. Our peds was very adament that he wanted him off of it by 15 months. It being his security in a big sense, I didn't want to stop cold turkey with him (though it was fine with my first because he wasn't so attached). Plus, I figured they say that breastfeeding is fine and good through 2 years old, so can it really be THAT bad going a little beyond 15 months with the bottle. He was done right around when he turned 16 months, a few weeks ago. So, what worked really well for us to break him of it gently was to put an ounce less in it each day until he really didn't care for it so much anymore...he didn't miss it after that. He could have as much as he wanted in a sippy cup with meals and snacks, but not in bed with him. I do have water sippy cups in bed with each of my kids. Allows them to drink when thirsty without the bad effects of milk on the teeth. Now, he really doesn't care about the bottle anymore...he just wants the drink from anything, doesn't matter what. He SEES bottles since I do home day care and one of the kids has the same kind of bottle, but doesn't lunge for them at first site anymore. :) He's just as well with a sippy. So to help your girl transition easier, you may want to do an ounce less of milk each day and instead of the babysitter leaving the bottle with her, leave a sippy of water with her so she still has something to hold and can take a sip if she wants without it being bad for her teeth and all.
I'd talk to the babysitter about doing the transition and tell her how it is that you really want it done, and maybe be open to her feedback on how it goes. She needs to be supportive of your parenting and you need to be comfortable with how your child is cared for. Like somebody else mentioned, I'd try to start the transition on a weekend, so you are starting it and can see how it goes initially and the babysitter has something to continue.
We used the Nuby's to transition my second son since he was so attached to the bottle. Honestly, I don't think it made him less attached to the bottle because it drinks like a sippy, not continuously like a bottle, if that makes sense. I'm kind of indifferent to them. It was nice to have the soft top originally, but they leak easily when the top is compressed(like bottles) and good for such a short period of time...then my son preferred regular sippies and I did too because he figured out how to leak it all over by compressing the top. Now we use them just for water once in a while.
I really don't think that her teeth sticking out is because of the bottle. She's only 18 months and 12-15 months is when they usually say to stop the bottle. She's not that far beyond. Plus, I think sucking a thumb or pacifier are more likely to affect the teeth in that way and those are OFTEN continued beyond 18 months. I'd doubt that they stick out because of the bottle. Maybe that's just how her baby teeth are meant to be. I don't know. You could ask the peds about it.
Best wishes to you!! Hope the ideas help!!