The good news is, your wonderful child is trying to learn how to develop complex speech and perspective, how to look at the world and how to treat people.
The age your daughter is at is the age kids start to develop to a deeper level whether they will see others as objects, enemies, or people. In fact, your time with your child now will determine the "quality of the road" so to speak your grandchildren will "drive" down.
Thank goodness these days we have resources that our parents and their parents could only dream of. It is a bit of a journey to pioneer, yet here are some invaluable book-gems. I Don't Have to Make Everything All Better by the Lundgrens is a great starting place. It's approach will transform what is going on so it feels productive instead of stagnant. The Anatomy of Peace by the Arbinger Institute will be a boon. You really are on the same team with your child. These take us from the dreaded role of master martyr to the longed for role of master peacemaker, both of which are very contageous roles to our children.
To step in your daughter's shoes for a moment, imagine being two going on three. Your complex socialization needs are beginning to emerge and the window for having those become second nature is going to be closing soon. As a child, your parents are the most powerful example you will have for good or ill and, in horror, you find out your parents are feeling all thumbs about the task. I think anyone would shriek =).
I hope you will get these books, or which ever ones others might post after me, give your daughter a kiss on the forehead, and let her know everything is going to be OK. (There are many valuable resources, these two are just the best I can think of for your immediate situation.)
So many of us are pioneering right now! So, relax, have some FUN with it, and know your daughter is going to be blessed!!!