I yelled and swat my kids when I felt it was appropriate. ALL of my kids turned out fine. If my three year old (that's shouldn't be "IF", it should be "whenever") I would yell at the hitter or kicker. If they kept it up, I would swat them. They learned if they gave pain, they got pain. That stopped the giving and receiving pain, quickly.
People the world over are motivated by pain and pleasure. If adults break the rules, they are given pain by all societies. (Speed and get a ticklet. Drive DUI and get a more expensive ticket. In Germany, the price of the ticket is based on your income. Running a stop sign for a poor man might be $100, but it made news when a very rich man got a ticket and it was over $100,000.) If Bill Gates got a ticket for $400, he would only smile and pay for it with spare change. I would have to eat beans and potatoes for a month or more.
The key with yelling or spanking your kids is to spend time giving them love and hugs when they are past the tears. Re-inforce your love with the words, "I love you, but you are not allowed to do ____", and then give them hugs. Of course you should tell them and show them your love on a regular basis.
When my kids reached their tweens and teens, they would ask that I drive them here and there or give them a this or a that. When they did, the answer was "No" if they didn't use "please" and "thank you". If they did ask properly, I would ask they knew why I was letting them have the keys to the car or taking them into town or what ever. If they said, "because you love me", then I knew they knew. If they said "I don't know", I would tell them, "Because I love you." Sometimes I would give them a hug.
That was positive re-inforcement and I think is part of the reason my kids and I have good relationships.
Good luck to you and yours.