Help me please

Hiya. Newbie here. I have a problem; my mum seems to be too attatched to my daughter and my daughter seems to be pushing me away. its gotten to a point where i just feel like im competing with her to win over my daughter. let me start from the beginning. I had an arranged marriage at 17 by family and had my daughter. Then the relationship went down hill and i got divorced and found someone myself. He is completely different to anything my family would have chosen for me but i was happy so i left home to stay with the new bf as family were totally against us. Since then my family members want 0% to do with me but still wanted to see my daughter. Im not the type to say no as when i had her my family took care of her more then i did. I wasnt given much opportunity to do anything as i was 'too young' family said. I once accidentally got water in my babys eyes when bathing her when she was a newborn (it was my 1st time) as soon as that happened i was never allowed to bathe her again. Slowly i wasnt doing anything and my mum was doing everything. Also at this time i was working 14 hours a day so my dghtr was very much attached to my mum. Since i left home mum has her 2 weekends in a month i have her the rest of the time but mum phones for hours at a time everyday to talk to my dghtr. When she goes and stays weekends or holidays she comes back and doesnt listen to me at all, pushes me away, tells me to send her back. My mum lets her do anything, buy her whatever she wants, does whatever she says, but with me she has to tidy her toys once she has played, feed herself, and goes to her naughty corner when shes answered back or rolled her eyes etc. So when this happens she would tell me that she wants to "go home to her mum" or "Your not my real family" and "nana lets me do whatever i want". I buy her something and she buys her something better. I dont buy her something and my daughter  tells me "i dont care i will tell nana, she'll buy me it" or "my nana loves me more then u." Just small things but they are starting to really get to me. I tried decreasing the time spent around my mums and reducing phone calls But even if my daughter isnt talking she will happily stay on skype for hours just watching her play. and mum shouts at me for telling of my daughter when she does something bad in front of her. Due to this my daughter acts up when mums around/on the phone. and doesnt talk to me on the phone when shes with mum as im not allowed in her house since i walked out So i can only contact via phOne/skype when shes there.  Please help. Sorry its so long.