Well, 3-year-olds can be notoriously feisty. Most parents have a much worse time with the terrible 3s than the terrible 2s. So chances are you didn't do anything wrong.
It does sound like she needs some structure, in terms of behavior, though. For most kids, a combination of rewards and consequences works well. As in:
1. "Pick up your toys, and you can have a strawberry."
2. "Uh oh, if you don't pick up your toys, then no strawberry."
3. "Honey, I asked you to pick up your toys 2 times. If you can't listen when I ask, then Elsa and Anna have to sit up here, on top of the fridge."
4. "Honey, if you want Elsa and Anna to come down from the fridge, then all you have to do is put your toys in the toy place, like this."
It's also really important to make sure she's getting enough food and sleep. Some kids need more sleep then others. Some kids have huge meltdowns, instead of just saying "I'm hungry."
Finally, I wouldn't just keep her in the house. The great big world out there can be a great incentive. Try taking her out. If she acts up, say "Oh no. That's not nice behavior. Looks like we can't go to the park after all today." Then, the next time, prep her: "We're going to try to go to the park again. But how do we act nice at the park? That's right! We don't hit. We use our words." That kind of thing.