I think that you need to strike some sort of a middle ground between babying your daughter, and your boyfriend's "teasing." Obviously you have recognized that your daughter needs to change. But your boyfriend does too! He is an adult, and should be able to modify his *BEHAVIOR* without changing his personality. Boys tend have a lot of teasing in their relationships, but girls not so much so--girls tend to affirm each other to show closeness. I have to wonder if your boyfriend's children are both boys, so he is used to the rough/teasing type interactions with them?
I think that you need to sit down with your boyfriend and discuss this issue with him. Acknowledge to him that you can see that your daughter has been overly "babied." However, point out to him that what he may not realize is that his size/voice/teasing can seem very harsh and scary to a little girl--even a non-babied little girl! Ask him to try and develop a relationship with her sans-teasing. Once they are closer, the teasing can gradually become a part of the relationship--to a level that she is comfortable with.
On the crying issue, one thing that works well with my 4th child (the first real "temper tantrum thrower") is to calmly tell him "I don't want my afternoon (meal, time with friends...insert appropriate description) with all this crying, so I'm going to take you to your bedroom for you to have some privacy to cry." Then I would carry him up--facing away from me--and gently deposit him on his bed. I reflect his feelings to him ("I know you are frustrated that your brother will not let you play with that toy. I know that makes you feel angry"), then I explain that he may come back downstairs when he is done crying. Sometimes at that point I will choose to snuggle with him--if I know he's had a hard day or just isn't going to be able to calm himself down.
I would also caution you to "pick your battles" on the babying issue. Drinking milk? I don't really think that is worth an hour of crying! I've chosen to simply not do "food battles" with my kids. I offer healthy meals, healthy snacks (or healthy drinks--your daughter can get calcium from sources other than milk such as cheese, yogurt, or Nutragrain bars if milk is an issue--offer her water to drink instead). It is up to them to choose to eat them or not. If they don't eat enough healthy food, they don't get "junk snacks." I don't do this in a manipulative way ("eat your carrots and you can have this candy bar") but rather in a pretty matter of fact way ("No, you can't have a soda. You didn't eat your dinner." or "No, you can't have a cookie, you've had enough sweets today. If you are hungry, go look on the healthy snack list and pick something else." (the "Healthy Snack list" is posted on the kitchen wall--my kids can pick unlimited snacks from it like fruit, boiled eggs, veggies & dip, whole grain crackers))
Hugs & good luck!
P.S. I just read Theresa's advice about setting a time limit for eating, then imposing a punishment if the meal is not completed. I can't begin to say how opposed I am to this. Our culture has enough built in issues related to eating that lead to eating disorders, we don't need to add others. I can only say from personal experience that this kind of approach to our kids eating leads to them learning not to listen to their body signals on hunger and fullness (so they may tend to over eat just to "clean the plate"), or on what foods are good for them and not good for them. I recognized in my mid-20's that I had issues with eating when I wasn't even hungry because finishing everything on my plate had been so drilled into me through the use of punishments like Theresa suggests. But it wasn't until I was 34 years old when I finally started thinging "you know, if I often get really bad stomach aches that double me over in pain after eating very wheat-laden meals, maybe I have a sensitivity to wheat" and guess what? I have Celiac Disease, meaning that wheat actually damages my small intestine to the point that I don't absorb nutrients from other foods well! I've had these stomach aches from when I was a child, and just dealt with them as "part of life!"