Do you REALLY want this to be different? From what I saw on the show, Leah and Ang seem to be okay with the situation. They have said numerous times that they are okay with Sophia waking up and tending to her wishes and giving her a bottle. There is no method that will work until the parents decide, and to me the parents have not decided on getting rid of the bottles. Once the parents decide, then the crying, demanding and the toddler blackmail will cease to be effective. Sophia may try to escalate but once the parents decide "this is the way it is going to be", things will get better and faster than you think. At the end of this message I have a suggestion to include and empower her in moving toward becoming a big girl rather than tricking or depriving her.
Here are some things for you to consider:
1. The bottle is a substitute for breastfeeding, how do you view parents who choose to breastfeed their 3 1/2 year old child with that child asking, whining or demanding "I want mommy's breasts". - I just want you to consider this and I am actually pro breastfeeding, I have 2 kids and breastfeed both of them at least to a year old. My first son I weaned at 13 months old and my second son I weaned at 14 months. They both moved directly to sippy cups.
2. You are now teaching Sophia how to deal with conflicts and rules when you try to enforce or change rules with a weak conviction. If you don't have a strong conviction, don't try to enforce the rule. You are making it more difficult for yourself and Sophia by first saying no and then through various tactics it changes to a yes. If you are going to say yes in the end just say yes from the beginning and at least project that it was your decision and not because she wore you down. This method at least gives some indication to Sophia that you are the decision makers rather than her. She is more likely to listen to your no's if she feels you are the decision makers. I think this is important because as she gets older, she and you will come upon more important issues - parties, curfews, etc. that you will probably want to enforce your decision rather than leave it up to her or have to endure more tactics (tantrums, crying, whining, etc.) as she tries to change that no to a yes. And just like Pavlov's dogs, intermittent reward systems are harder to change than consistent ones. Don't get me wrong, I am not advocating a strict - no love dictatorship but more like a benevolent monarchy that loves their people but needs to have rules for the society to function well.
3. You are teaching her not to rely on herself and her own resources to sooth and comfort herself but rather outside things. This is not an issue of nutrition but comfort and habit. And to some degree you are also relying on the bottle and sleeping in your bed as a comfort and soothing for yourself. When you can make her stop crying I think it makes you feel good and you can say you did that for her. But that means she is not doing it for herself. I feel that it is not any benefit to her in the long run to make her reliant on outside things or other people to sooth and comfort her. I also kiss my kids boo-boo's and give them hugs when the feel sad but they also need to go to bed when it is bed time and fall asleep by themselves in a dark room with the door closed and a cup of water (with a top for spillage reasons) at their bedside. They are not allowed out of their beds or out of the room unless they have to use the bathroom until morning. I feed good that they can do this for themselves and that I gave them the chance. There have been times when they have been awakened by a bad dream or afraid of the dark. I tell them that there is nothing in the dark that there is in the light and that he is safe at home and we are within earshot and available if he needs us. With this info they fall back asleep. My oldest has also recently gotten up in the middle of the night and said either he is afraid he can't go back to sleep or is unable to sleep. We gave him some suggestions like muscle relaxation methods and also to think of good thoughts or happy dreams and within a short time of leaving his room, he has gone back to sleep. For me, it feels good knowing I am giving him comfort but also methods and ways to for him to comfort himself. By being so concerned about hurting her feelings (because she is crying or deprived of what she wants) I feel that you are hurting her self confidence in being able to handle situations that are hard, difficult, uncomfortable or unpleasant. And I think you know that in life you will come across situations or people like these. I think being able to handle this as well as your own unpleasant emotions will actually make you happier and more confident.

Finally, if you are truly ready to make that decision, here is a suggestion: Use a charting system - this worked great for my son and potty training - I decided on a Monday morning that he is going to use the toilet and I put him in underwear. Every time he used the toilet and had his underwear dry he got to choose a sticker and place it on a chart. When he had an accident I didn't say anything but did place a slash mark on the chart to indicate a start over of stickers. He had one accident on Monday and one on Tuesday and was fine after that. For naps and bedtime I waited a little longer. When he was consistent during the day, I said that since he is doing so well with keeping his diaper dry during naps and using the toilet when he was up that he could advance in the big boyhood and wear underwear at nap. After a while of dry nap times, we move to bed time with the advancement to a grown up bed (a twin). Each time he was so happy to have mastered each stage and took ownership for his progress that we no longer needed the chart. I found out later from my boys that they viewed the slash marks as a negative mark even though I did not intend to use it that way. How you can change it for your own situation is move to a kid cup or sippy cup and every time she uses that to drink she gets to pick a sticker to put on her big girl chart. You can make picking out of charts, stickers and/or cups to be a big deal and have her help to choose. Every time she wants a bottle just give it to her but put a slash mark on the chart as a start over. At the end of the day look over the chart and give her lots of praise on how many sticker and/or how few slashes and she can see progress day to day. You can also do it in stages at nap and bed times. Have a special bedside cup (my kids have a cup with a lid and a straw so they can just turn and sip) and she can drink from it when she wants, this give her a sense of taking care of her own needs (this will probably work better if she was in her own bed but you could probably have her sleep near a bedside table so she has access). However you must first decide because if your not sure you want her to give it up, she won't be either.

Good Luck, I hope this gives you some things to consider and suggestions you can use.

Which ritual? Say that three times fast...
I mean seriously??? Is any of this for real? Even Rachel looked amused. Seems to me that people today don't care how foolish they look as long as they get some exposure. Look at all the reality shows.