I totally agree with Suzi. My first thought was why was she close enough to your face to dig her fingers into it? I've learned from experience that when a child is angry to put them down and if necessary keep them at a distance by holding onto their shoulders with my arms outstretched.
If she is having a tantrum and this sounds like one, then put her on the floor in a safe place and ignore her. I found that staying in the room but not paying attention worked best with my grandchildren. They are scared by their own intense emotions and became frantic when I left the room. I waited until they had stopped screaming, kicking, hitting. For me, what worked best at first was to sit across the room on the floor. When they were thru, they would crawl over to me and I'd hold them, not saying anything. Then, I would gently talk with them about what had happened. I'd sympathize with their frustrated and angry feelings. I would remind them of what had caused the anger and reinforce that this was the rule or whatever it was that started it all. Then I would get them started doing something else. I frequently took them to their room and gave them something quiet to do and they would fall asleep. The extreme anger of a tantrum is very tiring for the baby as well as the mother.
I suggest that this daughter is more strong willed than your other two. Strong willed is good but it does take a different sort of parenting.
If she has had enough rest, food, and ways to get out her energy, it might help if you can determine why she is so angry and find ways to deflect the anger before it gets so intense.
Often, at 2, the baby is working on becoming more independent. Up until now we could do almost anything and it would be OK with them. Now they want to have some control over their life. The need for this control is built into them. Because of this need they will eventually become independent adults. It's our job as parents to gradually give them as much control as they're mature enough to handle.
At 2 there are very few ways that they can be in control. We often have to think like they do, in a simple way, and create ways by giving them choices. Since you didn't give examples of when she gets angry I'll give some general ideas. Does she want to eat the banana or her cereal first? Do you want to play with these toys or shall we look for some others? Do you want to eat with your fingers or do you want this spoon? Give her a choice even when it seems like an artificial choice to you.
I suggest that if you notice when she is first getting cranky you can often avoid the anger by giving her a snack, providing some quiet peaceful time, and/or changing activities. Many bouts of anger are caused by the child being tired and/or hungry or being overly stimulated.
Also, many children need a set routine. Meals, nap time, and activities at close to the same time everyday. My granddaughter was flexible which worked well for me. But her brother was not so much so. I had to focus more on providing a routine for him.
I could take my granddaughter shopping. Shopping was a chore with my grandson. It was too much stimulation for him. He always had a meltdown. We could not take him out with us to eat if it was a restaurant that required that he stay seated. He just could not stay in one place for longer than 5-10 minutes no matter how many activities we brought with us.
In summary: 1) find ways to avoid the anger by being sure she has had enough rest, enough to eat, and ways to use up her energy. 2) Once she's started into cranky, provide what you think she might need; a snack, a nap, a change in activities, a quiet place to be before the anger escalates. 3) if she's having a temper tantrum, put her on the floor in a safe place, stay in the room but don't pay attention to her. Once she's calm, soothe her, briefly talk about what happened and get her started on a different activity or put her down for a nap if she's tired. I sometimes laid down with my grandchildren.
This to shall pass once their nervous system has matured some more and they've learned ways of dealing with their feelings.
Which reminds me of another skill. Often anger starts when they can't have a toy that they want or to do something. Early in the situation redirect their attention. Another many words describing ways to do that which I won't use now. :)