I'm sure you are probably concerned that your daughter is acting up because of your being away. However, the behaviors you are describing are very typical 2 year old behaviors. Children that age do throw tantrums. The fact that she throws them with you, is actually a good sign. Children tend to throw tantrums the most with the people they are most comfortable with. If she was uncomfortable around you or did not totally trust you she would be much less likely to throw a tantrum.
As far as being better behaved at daycare than at home, that is also very typical. Although no one knows for sure exactly why they do it, kids are almost always better for their daycare providers than they are at home. The leading theories seem to be that it is a combination of feeling much more comfortable with their parents, having the other children there setting a "norm" for behavior, and also the fact that daycares are set up with fairly strict routines and thus generally avoid many of the issues that occur in a home (you wouldn't want to raise your child like that at home, they need that more flexible time too).
That covers the why. As to how you can help her stop: You really can't, however you can discourage the behavior and help her learn better methods to deal with her upsets and anger so that the "tantrum" phase will be as short as possible. Here are the things I would recommend to assist her:
1. Put her feelings into words for her. For instance, if you see her throw a tantrum because you don't allow her to have something you can say "You really wanted that toy and mommy/daddy said no. Now you're really angry with mommy/daddy aren't you (or really frustrated, depending on how she seems to be)? This will help give her a way to tell you she is upset without throwing a tantrum.
2. Do not give in to something because she throws a tantrum, this will only encourage it. Help her through the emotions, comfort her, but don't change your mind about what you said.
Realize this is a normal phase, with your help she will push through it quickly.
If I can be of further assistance, don't hesitate to ask.