OP, I understand your frustration at being 'told' how to parent your child. It sounds very much like you 'give in' to what your mother wants to appease your mother.
Perhaps you begin with good intentions of doing things your own way with your DD, but then your mother steps in, and tells you where she thinks you are going wrong, or takes over completely, and you try to explain why you are doing what you are doing, but perhaps your mother doesn't take much notice so you take a step back because you are sick and tired of everyone being upset with you.
Is that kind of what it's like?
If it is, be very careful OP. If your mother pushes enough and you crumble and let your mother make the decisions wrt your DD, your DD will grow up to play you and your mother off against each other long after you have moved out. Your DD will see your mother as the person who is to be taken notice of, not you. Your DD will grow up to have less respect for you than she would have had if you had made it clear to your mother that it is your choice how you discipline your DD.
By standing up to your mother, you are clearly showing your DD that you are in charge AFA your DD is concerned, thus lessening considerably the chances of your DD playing you off against each other for years to come.
I also second what everyone else has said about moving out.
Also, when you let go of the reigns, and let your mother decide what will happen wrt your DD, does this make your mother realise her method of discipline doesn't work for you and your DD? I imagine not.
I don't think your mother is showing you much respect tbh, and what do you think it is showing your DD when someone who lacks respect for you is getting what they want, after showing you no respect?? 