I can sympathize with you for MANY reasons. I have 3 daughters (21-19 & 14 now), I was just barely 18 when I had my first daughter and my mother KNEW everything because she had raised me and my sisters...plus I was young and had no clue what to do (or so she thought). I could never do anything right when it came to my oldest daughter, my other two, my mother didn't care about at all. Games were and ARE still played to this day when it comes to my oldest...again, my other two don't have a relationship with her at all....my oldest daughter played right into my mother's games and I spent years completely frustrated because nothing I ever said mattered. It did come to a point that I had to keep her away from my daughter completely (it was out of a movie plot how twisted my mother is/was)...NOW my oldest has a daughter and my parents watch her during the day (much like your situation) and now all the games are being played on my daughter with HER daughter. She calls to complain about it but I can't do much for her...I spent years telling her how horrible they were to me because of wanting to spoil her and now they are doing the same exact thing to my daughter....it is a vicious cycle.
You are in a tough spot...I don't think talking to your grandmother will help, but you can give it a try....maybe if you tell her you need her expertise in getting your daughter to give up the pacifier or the screaming, she might take it better....if she is ANYTHING like my mother, she WON'T be told or even ASKED to do anything different than what she does...unless you NEED her help....it is ALL ABOUT CONTROL>
Good luck to you hon'
Just for the record....I AM now a grandma and I treat my daughter and granddaughter with respect....what my daughter says....goes....she is her baby's mom and I KNOW from my own horrible experience that it only causes hate and resentment when you fight the mom....and I have way more fun with both of them because I don't "worry" about how she is being raised...I TRUST my daughter and know she loves her baby....(I don't always agree with HER life choices...but she is an adult now....)