Some of the other responses sound good, but I wanted to add a little. I work with young children so I see this a lot. One thing I've noticed is that many kids do this with their parents but not with us as the teachers at school. But, as soon as the parents walk in the door, it all starts. This is because as teachers, we have to be firm and consistent with the rules or everything would be out of control. We teach the children what our expectations are and they know what the consequences are if the rules are not followed. We truly respect the children and they show it back. They know how to behave at school and we do not see as many behavior problems as parents do at home with some kids.
So, my advice would be to be consistent with your rules. Make sure your yes means yes and your no means no. Make sure your children know what the rules are (they can even help decide what they are). You can have a sign or poster of a few simple rules. She should know ahead of time what the consequences are and you need to follow through with them EVERY time with every child. She may test you at first to see if you are serious. Also, your consequences should be logical. For example, if she looses something, she doesn't get another one and has to do without. The consequence should be related to what she did in order for her to make the connection. However, I don't think every little thing deserves a consequence. Decide which things are important, and don't sweat the small stuff. Otherwise, all you will be doing is disciplining all day and that can do harm to your relationship. For example, if she is watching TV and is not listening to a word you say, stand her up, get down on her level, look her in the eye, and firmly say, "I need you to listen to my words when I talk to you" and then leave it alone. This will let her know you mean business.
Some parents suggested the 1-2-3 Magic book. I have not read it, but one parent told me what it was about. I would be careful about giving her 3 chances. This is telling her that you expect her to do it 2 more times before the consequence. Does it teach her an alternative behavior?
One thing we focus on at work is not what they can't do, but what they CAN. With toddlers-"You may not throw the block, but you can throw this ball instead."
Tantrums/tempers often mean that she is not able to appropriately handle her strong emotions. As adults, we have learned how, but we forget that kids don't automatically know how to do this from birth. It is something we have to teach them and help them learn how to do. Since you know your daughter the best, ahead of time, think about and decide on a method or plan of action that you think would help her. When the time comes that she is upset, follow through with your plan to help her calm down. Walk her through the process, talking about it, breathing deeply, whatever you think she needs. Be consistent and do the same thing each time so that she learns how to do it on her own. Talking about solutions after she has just calmed down but it is still on her mind can be pretty effective. Also validate her feelings--"You seem really sad/angry etc. right now." Help her put words to her feelings and this will make all her emotions less confusing to her so that she can express them appropriately.
Some of the most important advice I can give (and I've seen this really work) is to just have fun with her and let her see how much you enjoy being around her. Be silly with her and laugh a lot together. Sometimes in frustrating times, this is easy to forget. This will show her how much you love her and will also distract her from some of the negative behavior. This is especially important right now as it sounds like your family is going through some changes and she needs this to feel safe and secure. It will build a stronger bond between the two of you! Best wishes!