This this this.
Take the issue with the swearing just as a communication, a flag your daughter is waving as she is desperate for a better relationship with you.
She is a glass child.
YOU were a glass child - if your father hit and abused your mother then you were abused too. Your mother had to keep her head down and keep quiet. YOU had to keep your head down and keep quiet, OP. How many "Pandora bracelets" of attention did you long for, yet didn't get from your mother? How angry did it make you inside?
Now your daughter has to do the same- suck it up when there's something she doesn't like.
Those angry words and thoughts, "You're a lazy cow", "how did you become so entitled and ungrateful" "you'll pay for your rudeness"... listen to them echo in your head. Where do they come from? When did you, as a child, hear and internalise those words?
You were abused. You were abused.
But now you are abusing her. You're repeating your mother's coldness, because that's what you know!!! - when a mother is is overwhelmed by life and dysregulated, you learned, what they do is withdraw and become emotionally distant. And now you are dutifully doing what you learned.
Please get some really solid therapeutic help from a qualified psychotherapist, and do the hard work between sessions.
Don't kick off about swearing. Instead listen to her in kindness and tell your daughter some of this.
Tell her this - I was never allowed to show my anger, and as teens we have a lot of anger. I was punished. My mother was punished too, badly, and it fucked me up ( as we both know, sometimes saying fuck is a good expression of something intolerable). My mother withdrew from me when she was uoset and so it's easy for me to do that too. I did that with you today - and I am so sorry.
But I vow, I will make life different for you, because I love you, I love you, I love you. How did I ever get so entitled and ungrateful as to forget about you - that you, my daughter, so hard working at school, so polite and wonderful, are the best gift I could ever hope for?
Give it a try. Break the walls down.
OP you had a mother who was too overwhelmed to help you and care for you. So does your daughter. You have lots in common. Get help from therapy to love both of you as you deserve. You're the adult now and can break the horrible cycle of abuse.
I hope you do this work- do it for all your children and do it for yourself xx