A.R.
My daughter isn't my first child, but she is a little different. I adopted her from an orphanage, and when I brought her home there were some radical changes in her life. She lost the people in her world that she had lived with her whole life. In return she gained a new language, a new home and a family with totally new people in her life. I had bought a portable playpen for her to sleep in my room during her transition. One day she got into flour in the pantry and I just couldn't do it all at one time, of course she thought it was hysterical and kept going, so I put her in the playpen. She was still in the room right by me and could see what I was doing, not getting into trouble and still had some toys that were hers. It took a while to get her to understand the rules in a family, but she got the concept of the playpen being a time "in" right away. A time in's is where she is contained, redirected and she can see you and you can see her but she doesn't feel alienated from everyone. Although you can not talk to her during this. After she did this twice, all I had to say was "do you want to go in you're playpen?" and she stopped.
At 3 years old, you're daughter isn't old enough to understand that her place at home secure and she may be acting out because she isn't sure what else to do. For a child that has lost their "family" (and people living in the house feel like family to a child, no matter what the situation is), they need to know they are not going anywhere and they need to feel secure in who they are and where they belong. Will you kick her out of the house when she acts up? Will you love her no matter what? You and I know the answer, but she is 3 and just doesn't get it. When you do take her out of the playpen tell her in very simple terms, "this is not how we do things, we..." and make sure she appoligizes to the offended person.
Another trick the social workers in the orphanage used was to redirect the children rather than tell them DON'T do this and DON'T do that it was DO this and DO that. It sounds simple, but it's really hard to do. My son's and I still remind each other. After learning some new habits, I have found they are right, because as crazy as it sounds it works.
Good luck!!!