OK, so you know already that you shouldn't have read the diary. That's a pretty big breach of trust and a massive invasion of her privacy, so you might want to spend a bit of time reflecting on why you did that. What were you hoping to get from it? How do you feel about doing it now? And what have you learned from this mistake?
You said that your dd wrote that you break promises. Is that true? If so, can you reflect on why that's happening? Are you just flakey about stuff and forget to follow through, or are you making promises that you have no intention of keeping? Or is it that circumstances change and you find that you are unable to deliver in the way that you said you would? You need to get to the bottom of this, because trust is central to any good relationship.
Then there is the issue of the stuff that you said to her when you were arguing. She wrote it down, so it sounds like it was hurtful for her. Did you apologise afterwards and tell her that you didn't mean it, or did you just assume that she would know? How can you handle any disagreements differently in future so that they don't spiral out of control? Ultimately, you're the adult, so even if she pushes all of your buttons, you need to try to manage your reactions.
It is normal for teenagers to spend time in their rooms. It can be a bit hurtful at first,, as it feels like they're rejecting you, but it's a normal developmental phase. Try to ensure that the time that you spend together is enjoyable for both of you and that the interactions between you are mostly positive. Communicate openly and honestly, and don't be defensive about stuff. Pick your battles wisely and don't nag her about every little thing. Take an interest in what matters to her, and listen actively when she talks. Respect her point of view, even when you don't agree with it. Don't always take it personally if she is snappy.
Teenagers are fabulous. They are full of fun and energy, and they can be a joy to be around, but they can also be hard work at times. It's an incredibly difficult time for them, and they desperately want to know that you're still on their side. Be loving, be patient, be there. She still needs you, but the relationship needs to evolve and change from how it was when she was a little kid. You need to make that happen.
What she wrote in the diary was a snapshot of how she felt at one particular time. It's hard to say whether that's actually how she feels about you. She doesn't really hate you though. She wants your love and approval now more than ever.
This is a wake-up call. You need to work on your relationship and reflect carefully on whether your own behaviour is what it should be. It's likely that there is fault on both sides, but you're the adult so you need to step up.
Don't tell her that you read the diary, and whatever you do, don't ever read it again.