Keep up with the time outs. What you need to do (and this gets really, really old but it works like a charm) is when she gets out of the time out area (we used to use a rug because it was a set physical space for my son to "stay in") you need to use a calm voice and put her back saying, "when we are put in the time out space, we stay in the time out space so I will continue to put you back there until you stay." Be prepared for her to get right back out again, but continue and be consistent. She'll get even more mad, but after some time, she'll stay. Then set a timer (I think the general rule is like 1 minute for each year of their life: 2 minutes for a 2 year old).
When my son moved to a toddler bed he went through a phase of getting out of it whenever I put him down for a nap. This is how I solved it. I remember one time, doing the above scenario over and over again for 25 minutes. Eventually he stayed. All the while, I seriously stayed calm, taking myself out of the situation, knowing he was "learning" discipline. It worked in the end and within a few days, he was no longer getting out of his bed. He's almost 5 now and still doesn't get out of his bed.
Twos certainly exert their independence quite often, but they are trainable. Choices work great too. I remember my son standing by the car door opposite me one time refusing to come over to me to get out of the car (he wanted me to be the one who had to move to the door where he was). I, again in a calm voice, just said, "You can come over by me by yourself or I can come and get you, what is your choice?" He came because he didn't want me to be the one in control. If he only knew...=)
Good luck and stay calm!
V. Olson