You mention that your two-year-old daughter often wants your mother and not you to put on her clothes. On those given days, this preference may have more to do with how much time they have spent together. In fact, if your mom is the primary caretaker of your daughter while you are working, it's only natural that she would build up a close bond with her. These occasional preferences are just that -- occasional.
A two-year-old does not have the emotional maturity or intellect to "hate" a parent. Your daughter does not hate you nor does she not care for you. You need to examine your lack of confidence as a mother, perhaps feeling overwhelmed by your life as a young single mom and feeling that your mother is a better mom for your daughter than you are. Talk openly with your mom about your doubts as a mother. Turning over custody is not a well thought out response to your feelings of inadequacy as a mom. Your daughter needs you in her life.
I would strongly recommend that you investigate taking some parenting courses that focus on single parents and raising toddlers and preschoolers. You might also find great support in Parents Anonymous and other parent support groups. Ask your pediatrician, HMO, local children's hospital, area mental health center, and state department of social services for recommendations of such groups. Maybe you and your mom could attend a parenting course or support group meeting together. I am guessing that there are also other things going on in your life, apart from your role as a mom, that are causing you to feel poorly about your life in general. I think that you are carrying those negative feelings over into your relationship with your daughter. I'd really like to see you follow my suggestions and also consider going to see a therapist for some insights and support. Don't just expect your feelings to disappear on their own. That approach will not serve you or your child. Please write me with a progress report.