Tantrums occur when a person (of any age) realizes that their view of the world and reality are not the same. When a child has a tantrum, the child is struggling to cope with this difference, and adjusting their world view.
It is important for children to feel safe and loved, especially when they are having trouble coping with a reality that they can't cope with. When a child has an outburst, he or she is communicating to you that there is a problem. While you may not agree that the problem matters, it is important for you to acknowledge that to them, it is a serious problem. (Otherwise they will keep trying to tell you or anyone! Once the child knows you hear their pain, she or he doesn't have to broadcast it anymore. The trick to achieving quiet is to seriously let the child know that you understand the gravity of the situation in a way he or she understands.
Once the child sees that you get it, he or she will relax for a moment to give you a chance to solve the problem. (eg tell them that they don't have to drink the milk, leave the park, stop taking their sister's toy, playing with the oven etc.) This is when you have to either solve it or give them a coping mechanism.
About coping mechanisms. First identify your own. What do you do when you're stressed? drink tea, yell, have some quiet alone time to cool down, take deep breaths, call a friend, cry, go for a run, meditate, swear, drink or smoke....
Next identify which ones are appropriate for your upset child: take deep breaths, cry, have some quiet alone time to cool down.
The key is to teach your child to use these coping techniques on a regular basis, when she is not stressed. Then, when it's tantrum time, you can redirect.
Here's more from the American Academy of Pediatrics:
Also, choose your battles. Nutritionally and medically, two year olds don't need to drink cow's milk. Some 2 year olds have lactose intolerance. There is no need for milk after infancy. The American Academy of Pediatrics has a policy statement about preventing obesity in children.
It recommends that parents choose what foods are served, when mealtime is, and where it is served. Children get to decide whether they eat or drink, and how much.