Your DD is not you. Your DD is not your mother.
She is an individual approaching adulthood. She is in the middle of GCSEs which is stressful as well.
She is behaving like a teenager because she is one.
If she asks you for something do you just say 'no' or do you discuss why you want to say 'no'? How do you think that makes her feel? She probably thinks she is being completely reasonable and then you say no, that can feel like a knife into the heart for a teen in the middle of GCSEs with hormones ranging and trying to keep up with friends.
'Can I have a sleepover at X's?' doesn't deserve either a 'yes' or a 'no' it deserves, "well we have planned to do A, B and C so it's difficult this weekend but why don't you invite some friends over next week?"
As a teen if I asked my dad for something he would tell me to ask my mum who always said 'no'. So I didn't ask, I just did things behind their backs.
I know you don't want your relationship with your daughter to be like the one with your mother, but are you trying too hard? And are you actually forming a relationship with your DD or are you trying to make it the ideal in your head?
Her relationship with you and your DH is going to develop over the next few years and this depends on all three of you.
Sometimes we make decisions that seem like a good idea but are based on our own up bringing. Eg my dad was one of three boys, as a child he hated getting clothes as presents.
So my brother and I never had clothes as presents. But my dad was never a teenage girl who would quite like to have clothes sometimes.
I know that's a small thing in the scheme of things but is just an illustration of when, "I will never do this to /with my child" can actually be a hindrance.
I know it is hard and they don't come with a handbook.