Oh Dear Sheila, you do sound so down. Poor you, your instinct is probably right, that it is more than just the terrible two's or three's. Can I ask a few questions and give hypothetical answers. Your little one sounds like bright spark and this can cause the terrible three's to be explosive, as a friend of mine found out, due to frusrations. The first thing I ask is do you go to her when she is in a tantrum? Is it because you get too close to her that she is able to bite and kick or does she get up and come at you? If you go to her, then you are empowering her, giving her attention, she may see that as a positive and it allowes her freedom to escalate the tantrum. If that is the case, then I find walking away, but within sight, and calmly telling her that when she is quiet and calm you will come back and talk to her. Does not matter if you are in a shop, just walk to the end of the isle.
It sounds also like she is a little unsure of her boundry markers now that she is a little older, can you tell when a tantrum is about to escalate at home? Can you dive in before she hits the floor, pick her up and take her straight to the naughty corner before she has time to let rip. If she wont sit on the step,stool or whatever you use, you may think about giving time out in a safe room, where you can hold the door till she is ready to talk. A lot of adivice say's give time out for the age of the child, but some children are very strong willed and need time out till the tantrum subsides, and calm is setting in.If a child is still in tantrum mode after 3mins, then they are not yet ready to listen. We cannot communicate with kid's who are not in listening mode.
A combination of time out zone and sticker chart may work, but you would have to be rigid about the give and take. My friend took to taking all toy's away that were thrown and putting them on the naughty shelf, her little boy got them back through earning stickers for good behaviour throughout the day.
I also see that you are in UK, if you go to your health visitor she will be able to put you in touch with her local behaviour Psychologist. They are great for helping out when children are setting their own boundries and can help you both to work out a set of boundries that suit both your natures.
I am sorry if this is not very helpfull, but please dont suffer in silence, the NHS is there to be used, make the most of it if you can, you help pay for it,hun. Thinking of you.
Best wishes, I hope you find some answers soon. Luv,Winnie.xxxxx