I would let it go if I were you. She just turned two - and that's pretty young for a kid who is attached to the binky. It's not as though she were heading off to Kindergarten or anything. Give it six months. She might stop on her own or at least be ready to let it be coaxed away from her.
I felt the same way with my daughter - I wanted the binky to end and she wasn't ready. You have to ask yourself if there's really a good reason for taking it away (like it's messing up her teeth or something) OR if it's just all about YOU. For whatever reason, YOU feel it's time to end it. But she might really need it for security right now. Maybe you could put up with it for a few more months...?
As for the night-time screaming... If she's in a crib I would think she could be trained to find the lost binky on her own. My son always had to have little cars in bed with him and would wake up if he lost one. But as long as the sides of the crib were blocked so the car couldn't fall out, he was able to find it himself and go back to sleep.
So next time she wakes up crying, don't give it back to her -- instead talk to her and tell her to look around for it. Make her find it herself a couple of times and she'll get the hang of it. Good luck - there are so many little frustrations like this!