You are being very unreasonable!
I was born Kathryn, and everyone who reads it aloud pronounces it Kath-rin, rather than Kath-er-in like they would if it were spelled Katherine or Catherine. I HATE the pronunciation without the middle E sound.
My chosen name is to go by Katie, it has been for the past 25 years, its what i sign birthday/christmas cards from, have as my social media name, sign off emails with etc. Despite this, my entire extended family called me (I'm NC with everyone but my dad and sister for the past 8 years) Kathy. (my late paternal grandmother would even spell it Cathy) I despise how Kathy sounds, its the worst shortening variation of my name in my opinion. It was even more hypocritical as they had their own name gripes, my paternal gran went by a shortening, my maternal gran went by her middle not first name, one aunt wanting the shortening and spelling Jacky instead of Jacqueline or Jackie, and other aunt was Linda not wanting her name shortened to Lin. I respected their name choices, but they never respected mine. It still angers me when i've had no contact with them all this time, if it were my own father insisting on calling me Kathy, i'd be very upset, and feel completely disrespected. Resentment would grow every time he used his choice over my choice.
This would be a very silly hill to die on, do you want to estrange yourself from your child and have her limit contact with you, over something as small as a slight pronounciation change for you, but that's mightily important to her as her whole identity? She's not asking you to call her a completely different female name, a male name, to call her he/him/son etc.
It is also massively relevant that this is the pronounciation her father and fathers family (and general public if thats the common pronounciation in her country of residence) has used her entire life, to her it is as much her "correct" name as the way you feel is the correct way. (It sounds like you chose her name without her fathers input, so the one way of "correct" pronounciation wasn't agreed upon from birth)
At the end of the day, it is HER name, not yours, and it is her sense of self identity you're trying to knock down and replace with your version, telling her "I'm right you're wrong, because i'm your mother" and in my opinion, that just isn't your right to decide.