K.R.
Dear W.,
You are not the worst mother of all time, you just feel your child's heart, as a good mother does. And you want to fix it !
Our fast paced American society sometimes tries to push us and our children into a life that is too fast paced and self serving. It seems to me that a 3yr old is too young to push away her parents, though this is a naturally independent move on her part at this age. What is missing today is a strong bond of family in society, and the sense of living for and serving others. Sometimes we have to pull ourselves and our children back into the family, the first school of love. From my own experience raising a strong first born daughter you have to project the positive. Our children learn a lot from their parents by observation. I always tried to change my (poor me, my poor child mindset ) and/or keep my emotions to myself about the situations you mention, just involve her in more positive situations. Do you have a faith based organization you go to once a week ? Is there a preschool nearby where she could go for a few hours ? Do you have a pet ? A puppy might be a good place to start with responsibility to something other than herself, like making sure the puppy has fresh water daily.Of course it will be up to you to take care of the pet and share the responsibility a little at a time.
Your daughter may have already a high standard of a friendship relationship which others may fail to come up to, but just tell her to be the friend she wants to have for someone else. Talk with her about her experiences and how it makes her feel and guide her to see how to be a happy person others will naturally want to be around. Not a give to get, but just a "happy, secure in the love of my parents" kid.
Once again, children learn the mindset of their parents when the parents are unaware, so it would behoove us as parents(not just mothers but dads,too) to make a good picture of health and happiness that they are seeing. Children are for growing and stretching our hearts, our education, too. Hope these thoughts help, from my experience. My daughter just graduated from university and is married so I am looking forward my grandmother and good inlaw stage. Wish me luck !