Hi J., there is definitely a solution!
We have four children ages 13, 11, 5 and 3 and we use Nonviolent Communication as taught by parenting coach Bill Stierle.
This process has a few steps.
The first step is to validate the child's feelings and get him to agree with you. With my 3-year-old, she may be yelling at first, upset. So I say,
"Are you yelling because you want mamma to hear you?"
She usually says, "Yes!"
Then identify the need, it's important to get your child to agree with you three times. This seems to really diffuse the anger/ intense emotion to know that their needs are being heard and understood.
"Are you disappointed that Mama didn't give you the toy?"
She says 'Yes!"
"That didn't meet your need for choice, did it? You want to choose to have the toy?" (Choice is a big need for children and identifying the need is important here).
Once you get your child to agree three times, I find that this quite often diffuses the upset. Sometimes I repeat the process. Then it's important to establish that you have needs too.
"When you scratch yourself, that doesn't meet Mommy's need for safety for you. Can you say safety?"
Or
"When you yell at me that you hate me that doesn't meet my need for kindness. Can you say kindness?"
The idea here is to get your child, over time, to start understanding that 1) their needs are valid and that 2) other people also have needs. They will start learning the language of needs and nonviolent communication.
Sometimes you may feel so overwhelmed in the moment that you need to empathize with yourself before you can empathize with your child and figure out and acknowledge their needs. So you may want to take a moment in your own head to think about what needs of your own are not being met by your child's upset. In your own mind you might think, "My need for peace is not being met." or "My need for kindness is not being met." Sometimes we feel like our child SHOULD know better, be better, etc... and this is where we start getting into trouble. To acknowledge your own needs not being met in the moment, self empathy, can go a long way to help you to feel centered so that you can help your child learn to work through their emotions with the new vocabulary of words that you are teaching them instead of with hitting, kicking, screaming, etc...
After your child calms down, if you can get them to acknowledge your needs too, that's the ideal. However, they are still learning the concepts and idea that others have needs, even if they resist saying the words back to you in the moment. I know that we also have a need to be heard and understood and it can be frustrating when we feel our child SHOULD learn this quickly, acknowledge us right away, etc...
It can be hard to learn a new language like this, but really, it gets easier and easier the more you do it.
Here's a link to some resources on Bill's site if you're interested
http://www.billstierle.com/parentingresources.html
Cheers!
K.