D.K.
At 21 months she is not disobedient, she is learning about her world. Your job is to encourage this while setting safe boundaries. She hits because she is frustrated. Much of what you do is simply tell her 'no hitting' and then distract her with something she can do. You will have to do this three to four million times and she will eventually learn (or get old enough that she doesn't do it anymore).
Throwing can occur for several reasons - one is frustration - you need to distract her with something she can do.
Another reason is curiosity - it is fascinating to them to see what happens when you throw your food out of your high chair. Over and over. You can give her things she can throw (soft balls, stuffed animals etc) and if she is primarily throwing food, you give her only a little bit at a time. When she stops eating and starts playing with it you announce (in a completely non-punitive way) I see you are done eating and you take the food away.
One thing that can work well is playful parenting - make what you want her to do fun. Oh, it's time to get dressed, I bet I can get to your room first. I bet we can't get your shirt on before I can count to 10.
What things are you telling her to do that make her scream? Many times the things that help are:
1. treating her with respect- think about how you would feel if your boss wanted you to do whatever you are instructing her to do in the way you are instructing her. If you wouldn't like it, she won't either - so rephrase it.
2. Giving her two positive choices - we need to clean up the room - do you want us to clean up the stuffed animals first or the lego? Only give her a yes or no choice if the no choice is acceptable to you.
3. Giving her time warnings before transitions - we are going to need to clean up your room in 5 minutes. And then another warning at 1 minute. Toddlers get truly engrossed in whatever they are doing and do not find it easy to just stop what they are doing because you have decided it's cleani up time.
4. Do it together - she is still too young for you to tell her to go do a lot of things and then expect that to happen. She needs you to brush her teeth with her, clean up her room with her and work together on most things.
A tantrum means she is so frustrated her brain has shut down. No learning occurs during a tantrum so it really does nothing other than frustrate an adult to try to 'teach a lesson' during one. A tantrum will end eventually - a child left alone during one may stop spontaneously if distracted by something or simply wear himself out from exhaustion. IMO, they stop faster if you reconnect with the child, get down on their level and ask if they want a hug or just to sit with you. Once they are over it, you can address whatever the original cause was. For my son this did not encourage more tantrums (he probably only ever had 2 or 3 that most people would call tantrums).
I do not do time outs and have never done 'consequences' logical or otherwise. They made no sense to me. I also did not force DS to say he was sorry for something - I would model that behavior to encourage it. But I think that forcing a child to say sorry to get out of time out just encourages them to lie (no they don't understand lying at 21 months, they understand pleasing a parent by saying sorry).