Most 4 year olds are active. Sometimes very active. I run a daycare and NONE of the 4 year olds take naps. Most have short attention spans. Before this I spent 10 years working with children in the mental health field where I worked with a lot of children with ADHD. I would hate to see a child labeled with ADHD at this young of an age. I'm not sure that people realize that it can affect their ability to get certain jobs when they become adults. Or to get life insurance.
That said there are some ways to deal with it. Some you may do already, I can't tell from what you've written. But I'll make up a list for you and hope it helps. In my experience helping a child with any serious problem is a lot of work for the parent and hard so don't be discouraged. It is not immediate fix. It's not medication, which in my mind is sometimes necessary to counter a chemical imbalence, but also the last step. I'm going to tell you about behavior modification which takes a lot of time and months to complete. The teacher on here who responded was right on the ball I'm just expanding on her advice. And it will get worse before it gets better but when it gets better it will be worth it!
1. Become structured. Very structured. My guess is you already are to some extent because you work you have a routine for getting up in the morning and getting ready or you would never get there on time. But make sure it's well organized. Every morning at the same time do the same things. It will give your daughter a sense of security but also enable her to learn the routine and begin to complete it on her own.
2. A timer is your best friend. I use it with my own kids who do not have ADHD. You can use it for time outs. You can use it to time activities (ok you have 5 minutes to brush your teeth. You have 10 minutes to play before we go. When the timer rings we're done.)
3. Start using time outs. A time out is not just sitting in a corner. It is a time away from an activity that it getting out of hand. Of course it is still also used to redirect a behavior and used as a consequence. Use 1-2-3 magic. Start by asking for the behavior to stop (Please don't jump on the couch. Jumping continues.)Count 1. 2. (If behavior doesn't stop go to 3 and guide the child to time out chair which should be set in the most boring no toys or tv place as possible.) The time out should be the child's age. They are not to talk during it. You are not to respond. Please explain this to your child and walk them through what a time out will be like before you use it for the first time and before there is a problem. Explain "this chair is to help you calm yourself down." If the child talks or gets up the timeout starts over again. The first couple of times don't be surprised if a time out takes a very long time. The better you explain this (and have her repeat the explanation back to you) before you need it the smoother it will go.
4. Make a behavioral chart and a reward system. Pick out the top 5-6 things you want her to work on. (Such as listen to the teacher.) Don't expect her to get all of them. When I start this I do daily rewards and then weekly rewards. For instance Get 3 stars a day and you get a sticker for your sticker book. You get a 1/2 hour of computer time. Something easily done that isn't too expensive but will be rewarding for your daughter. Get 20 stars a week and get ______________.
She will Not get the weekly goal for a while. But it is something to work towards. Something rewarding. And make sure you do it when she reaches it or she'll learn there is no point in working hard (and you can't be trusted). When she is getting these done consistently enough change to new goals. Check in with the teacher to make sure she is still listening in class or whatever the goals were. This is going to put extra work on the teacher but the end results will be a child who does not get kicked out of preschool for behavioral issues.
5. Start girl chat time. This is a time to talk about everything that's happened during the day. Special time. Get out the hair brushes and barrets and sit on the floor and be together being silly. It can be 10 mins if that's all the time you have. Use phrases like, "What else could you have done?" Exploring alternative ways to behave and even role playing them will help create new ways to deal with difficult situations. "Why do you think they got mad? Would you have gotten mad?" "What can you do to make it better? What about...?"
Well, I know this is a long note but I'm trying to cram college behavioral psych into a little note. This is also a very short list. If you want a great book written for the average parent it is SOS Help for Parents. It's great. It spells everything out. Techniques to deal with most problems. And it's reassuring that things will be fine if you are mom.
We can be friends but first we're parents. Good Luck!