It's not easy. Don't let anyone tell you it is, or that you just need to discipline them better. They don't understand that it doesn't work that way for our kids. I have an easy time with my kids compared to you. I just wrote a post about potty training and how I used a give and take away system with my son. It wasn't easy, but we came up with a system that worked for us. It sounds like you need to come up with a system that works right for you.
For three kids, it is tougher for you. You might want to take some time and set up schedules that you can post on the wall. You can give each child their own schedule to follow for each day. This will help with the short attention span. Assign activities for each to do and chores that need to be accomplished. They can check them off as they complete them. To help with transitioning, you may want to try using a timer. Set the timer for the amount of time allowed on an activity, and when it goes off, it is time to stop and clean up or turn off what is being done.
To help with cooking, let the decisions be yours. Have them stand on paper and trace their feet on it. Have each child's name on the papers. Tape the paper on the floor where you want each child to stand. Make or have your kids make, ingredient cards for your common recipes that they can help you with. Each time you are going to cook with their help, pull out the ingredient cards that apply to the recipe. You can have them pick the cards by random before starting. You can make cards for mixing, pouring, opening, too. Now, here is the tricky part. Put a chair in the kitchen. If one starts to fuss or complain, it's an automatic minute in the chair. Or, they lose a card.