At this age, your daughter has strong emotions and is not quite sure how to show or handle them. So, they erupt as tantrums. You can do several things to help her get through this time.
First, understand that she does not know how to effectively and appropriately handle all these strong emotions. You can help her learn how to do this. It is a learning process. She may need some time to get the feelings out through a tantrum, just ignore it, let her do it and make sure she is safe. Definitely DO NOT give in. This teaches her that what she is dong effectively gets her what she wants.
After she is calm, talk to her about her feelings. Say, "I understand that you are very sad/angry/mad. It is not ok to scream and behave that way. When you are angry/mad etc. you can use your words to tell me (or whatever you want the alternative behavior to be)." Basically, you are validating her feelings (remember, it is ok to feel that way, but there are appropriate and inappropriate ways of handling those feelings); telling her what is not acceptable; and then giving her an alternative and acceptable way of handling her feelings next time. Be consistent! Validating her feelings and using words to describe them helps her make sense of all the confusing emotions.
Before conflict arises, you can give her choices to avoid the unacceptable behavior. "Do you want to clean up your toys by yourself or do you want me to help you?" Either way she is cleaning up and it doesn't really matter if you help or not. Give her two choices that you are ok with and let her choose. Letting her have more choices throughout the day can help her feel a little more control over her world, but not an overwhelming amount. As for the situation this morning, the two choices could be "I can either lay with you for a few minutes, or you can choose another stuffed animal to have in your bed while you go back to sleep. You can have milk in the morning." Then, stick to your choices. If you feel you might give in (like when it's 4 am and you just want to sleep) then at least make her ask nicely (using her big girl voice) and don't let the fit be the last thing that made you fulfill her request. I still don't recommend giving in either way because it's inconsistent, but sometimes you just need sleep!
Remember that having a strong will is not always a bad thing. Later in life, she will never be a pushover. Your job right now is to help her learn how to use that strong will in a useful and respectful way. As an adult, you would probably want her to be able to voice her strong opinion with co-workers respectfully without offending them, and also be able to get her ideas carried out. Think about what you can do NOW in order to hep her learn these skills. Help her to also learn about other's ideas and opinions as she grows. Look for opportunities where you can describe what another child may be feeling. For example, if at the playground you see another child get pushed or hurt, explain to her that the child must be feeling pretty sad right now. What's something you could do to help them feel better? Talking about and naming her emotions and other people's emotions (on TV, in public, etc) can help her work through this.
As far as the bottle goes, let her pick out some new sippy cups and get rid of the bottles (or at least hide them). If you don't have them anymore and she knows it, then it can't be an issue for long. Does she have a stuffed animal or blankie she can use at bed time instead for comfort?
Hope this helps a little, let me know if you want to talk more about this. I work with young children at a child dev. center so I see a lot of tantrums!
Best wishes!