You need to get hold of this situation quick. If you are yelling or screaming, you have lost the battle. If you tell your kids something 1 time and they do not respond, the 2nd time you need to TAKE them and DO whatever it is WITH THEM and get it done. If they proceed to throw a tantrum you, must keep your voice quiet and remove them from the situation(if in public), or put them in a place, (room, chair) where they do not get to do what they want, but must wait until they are willing to do what they need to do in a respectful manner.
I suggest that spanking always be a last resort. Keeping your voice quiet and your composure will drastically help the situation. Try to keep yourself calm, because as soon as you lose your calm, you've lost control. If 1 child starts acting up, it is time for everyone to pack up and go. It may seem harsh for the other children, but they will live through it and they will learn from the situation and it may help to keep the others in line next time, so they don't lose out on play time. Being strict won't work if it means you yell directions at your kids and expect them to obey. Children have to be taught. Give them rules as well as guidance. You have to teach them to do the things you want them to do. You can't just say "Do this or this will happen." Show them what to do the 1st time, help them do it the 2nd and maybe 3rd time, and supervise them the 4th and maybe 5th times. By then they will probably be doing it on their own. If one starts throwing a tantrum, everything stops, you should become quiet and calm and walk them through what you need or have them sit and wait until they are calmed down, before you go any further.
If your buttons are easily pushed, this problem won't go away quickly. If you have time to sit down to the computer and type out a question, you have time to sit with your child and QUIETLY hug them, talk to them, soothe them and if necessary because being calm isn't working, sometimes just stop paying VISIBLE attention to them until they get themselves under control.
You need to practice on this and talk yourself through situations you've been through before, that you know will happen again, and practice how you will act and what you will say. When it happens you are better prepared.
Unfortunately, some of your children will experience some form of punishment or denial of play time, etc in order to get another child under control. That is just part of being a family. When the kids realize that they are not going to get their way until they respond what you want, they may just have to do without a few things.
You also have to be prepared to do without some of the things you like, because you have to learn to control your children. That is also part of being a parent. If you yell and scream at your kids, so that other people around will hear you trying to discipline your children, you are making a fool of yourself and being annoying to those around you. If you remove yourself and your children from the situation, control starts changing to your decision and not the kids. You children need to learn respect for you as well as for others around them. Respect is always a 2-way street. YOu must show your children respect when they earn it. We live in a world where we are not the only ones here. You also need to respect those around you, by being able to control your children.
I had 2 boys of my own and took care of 2-4 other children every day. Spending time communicating with them and not just at them is the best place to start. Listening to what they are saying, not just hearing the sounds that come from them. Responding to them as if what they say is important to you, makes them feel as though you are paying attention to them and gives them confidence in themselves. They will after a while be able to talk to you without screaming or throwing a fit, because they know that when they talk to you in a "indoor" voice, you will actually listen them. They don't feel the need to scream or throw a fit to get your attention. When your children talk to you, RESPOND to them, even if you are busy. If for some reason you can't verbally respond to them, try smiling and giving them a "just 1 second" signal. That way they know you heard them and that you will respond to them just as soon as you are able. It will take a few times for them to understand what is happening if you haven't done that before, but they just want to be recognized, most of the time.
If you are going to be on the phone or visiting with a friend, talk to your children first and let them know this is a time that they need to not interrupt unless it is an emergency. Let them know what your "just 1 second" signal will be, and ask them what they would like to do while you are busy, so they will have some form of entertainment. Then they will know that even though you are going to be busy, you thought of them first and that if they truly need you, you will not ignore them. They will always "test" you at first, so it will be another learning process, for both you and them.
Sometimes, when they come to see you and you are engaged with someone else, a hug, pat on the head, smile or little kiss just acknowledges them and they won't have to interrupt, because they see that even though you are busy, you are seeing them and thinking of them. That may be all they want. Sometimes, it is nice to even allow them to be included in a conversation from time to time. Sometimes you will be amazed at what a 3 or 4 year will say, that is right on target with your conversation.
May God richly bless you and your children and may His loving hand guide you through this time of teaching and respecting your children and that He will help them learn patience as well.