S.,
I think you have been given some great advice about prevention, so I will give some for those times when prevention doesn't work.
Children do what works to get them what they want, and if your child knows that she will either get what she wants or bring you to your last nerve by screaming, she will.
She is certainly old enough to learn that the world doesn't revolve around her and that she can't command the universe. And actually, as much as children look like they want to run everything, they really don't. They are trying to see what you are made of, what you can stand up to and how strong you are. And if you cave to the tantrum of a 4 year old - how scary that is for her - she needs someone to take care of her who is strong enough not to cave to anything. That is a part of "testing the limits." They act like they want that power, but they really don't because it is too scary to handle.
I like the "love and logic" method. There is a book you can buy and some school districts offer parenting classes based on it. It is in there with the "tough love" philosophy. If she doesn't like what was fixed for her to eat, she doesn't eat. No battle, no forcing food, and definitely no separate meals or snacking later. Children will not starve themselves. Eventually she will eat.
And you and your husband are the head of the household, not her. She should not be "wearing the pants" in the family. If she tries to command where you go and what you do, she goes to her room with the door locked until she can show you a decent amount of respect. If you have to, strip her room so she doesn't destroy it when she is in there. She can earn back every piece of furniture, every toy, every picture on the wall.
When she does calm completely down - and recognize that for a while it could take hours or even overnight, so don't feel guilty - then you calmly talk to her about appropriate behavior and consequences. Then you reaffirm her, cuddle her, hold her. Make sure everything is good between you. But none of this can happen during a tantrum.
Some things kids outgrow with time, some get worse if they aren't taken care of. This falls in the latter category. She is just going to get bigger, smarter, stronger and have access to more as she gets older. Sure, she may not scream at the top of her lungs every minute because she will learn the hard way at school that it isn't socially appropriate, but that "my parents are doormats" mentality will stay. When she is a teenager you could very well have trouble that makes all this look like a walk in the park.
You will do your whole family a favor by being strong and setting some good solid boundaries and holding her to them. Don't feel guilty. Good parenting doesn't mean giving into everything and being popular. Good parenenting means you love them enough to do what is in their best interest and preparing them to be self-sufficient, independent, loving, unselfish adults who can handle life's difficulties and contribute to society.
Best of luck,
S.