Hi, there! I just saw the show, and your struggle to get Sophia off the bottle. I am a mother and have a degree and experience in this area. It appeared from what was on the show that there was a key element missing in your attempts to help Sophia sleep without the bottle. Since Sophia is 3 1/2 years old, she is old enough and bright enough to realize what is going on...it was even talked about on the show. Since she has this awareness, it is imperative that you sit with her and prepare her for being a "big girl" which means, among other things, that she does not "need" the bottle anymore. If she buys into the idea of becoming a "big girl", you will have much more success. There are several ways to do this, but I would suggest that you buy some picture pooks and stories about what it means to be a "big girl". There are books like this on every topic...potty training, eating healthy foods, sleeping in her own room, and yes, ditching the bottle. When she has bought into the idea that she is not a "baby" (and make it clear that only babies drink from bottles), she will want to be a "big girl" (be sure to show her all the privileges big girls have that babies don't). When she is ready, have a ceremony where she can participate in getting rid of the bottle. You can do this by putting the bottles in a basket hooked to balloons and having it float away, putting them in a special box, or simply having her throw the bottles in the garbage and taking it out to the trash can. Once this is done, go to the store and pick out a special "big girl" cup that she can keep by the bed to get a drink of she is thirsty. Be sure to make a huge deal out of this so she can feel proud of the decision that "she" (wink, wink) is making. And be sure that all friends and family members tell her what a "big girl" choice she is making, and that everyone is proud of her being a "big girl" now. You two will have to do the work to help her understand that she does not need the bottle, and encourage her to be a "big girl", but once she buys in to the idea, I'm sure that she will suprise you by making the choice to ditch the bottle.
Good luck!