I suggest that you take her for a physical checkup. It's always a good idea to see if there's a problem you didn't know about.
You may have to take some time from your regular schedule (and I don't know what that is) to concentrate on this situation. Toddlers don't respond to deprivation as older children do; they don't necessarily connect it to behavior. Toddlers don't have right and wrong straightened out in their minds yet; they just have "I want" and "I don't want," and you know it changes by the minute! It's also not unusual for two-year-olds to have meltdowns about anything, everything, and nothing. It seems to be in the job description to have a certain number every day!
So you might need to say, "Today is the day we're going to stop hitting and pushing people." Every single time she does something unacceptable like that, she goes into the time out corner, with no lectures or extra attention from you - pick her up, set her down in the corner, that's that. After a minute, ask her if she can come out or if she needs to stay there longer. If she goes back to playing and acts up again, whether it's thirty minutes or two seconds later, do the very same thing.
You may certainly assume that you will not get anything else done during this time. And she'll test you to see if you really mean it, or if you'll give up, or if you'll cry or get mad. You may not want to have company over (although she'll test you later when they do). The family will be enough to start with.
You could even surreptitiously time the periods when she does *not* hit or push or throw, and be able to say, "You made it for forty seconds this time," or, "You made if for one minute and twelve seconds." The idea, I'm thinking, is that hopefully she might become interested in what is happening to her instead of her impulsive feelings (or the habits she has gotten into).
I can't guarantee that this will work. But it might. Be sure to handle her with calmness, and even with humor. She's not being taught because Mama is angry or upset. She's being taught because she is not treating people properly, and needs to learn how to do it.