My only reservation about the idea of giving the cups back is that you will be teaching her that "sending it away" is not a permanent solution. What happens then? You give them back, she realizes that these are the same cups that the babies were suppose to get... and she discovers the ruse.
And then, how do you take them away again?
If you do go to the store and buy *1* new sippy cup... What about not filing it up? If it is her security item, does it really need to have liquid in it? Maybe just having it will help soothe and you can still focus on other cups, getting her weight up, etc.
Oh... Have you tried straws? I know, not environmentally friendly... However I was having a hard time with my DD and found that she was particularly excited to use a straw, especially if she can choose the color and put it in. We use the sippy sup sport bottles but without the straw that comes with it (because I'm not good at always cleaning all those parts and I think its more hygienic if she uses a plastic straw).
Good luck!