Adriane letting go is so hard, especially of the person who has been your best friend.
FWIW when my partner of 10 years cheated, I knew in my heart what he'd been up to - the only proof I had was that he'd gone somewhere with this woman (I'd known her for years 
). He refused to admit anything hadactually happened even though we were splitting up anyway. A well-meaning friend actually locked the pair of us in his house in an attempt to get is to talk! All I had to say to him was "admit it" and he wouldn't, so I just ended up watching the TV and ignoring him, until my friend let me out.
Eventually, days later, he admitted that they'd got as far as the bedroom, but then he'd thought of me, and couldn't go through with it. 
Which I believed for about 3 minutes, then realised it was a total crock of shit.
Eventually, he did admit it. It took about 2 weeks. (They were still seeing each other all of that time).
I don't know why he took so long to confess. We were so obviously splitting up anyway. I think he just didn't want to deal with it, and tried to weasel out of it when confronted, with no regard to the obvious fact that stringing it out was it was making it worse.
In retrospect our relationship had been over for a long time, but because we had been so close for so long, it was really hard - for both of us - to let go.
I'm so glad we did though, as with the benefit of hindsight I can see how dysfunctional that relationship was, and I'm so glad to be out of it.
Of course I may be projecting - and my sincere apologies if I am - but it does seem, from the outside, with the limited information I have from this thread - that this relationship is over really, but that you are finding it hard to actually let go.
"The reasons he's giving for leaving the relationship are so trivial (it is complaints about how we hang up our coats and where we leave our shoes), it would be such a waste to throw away our lives on them. He's fixating on the little things that annoy him and not on the positives of what we have."
He sounds to me as if doesn't want to focus on the positives.
Do you think it might be possible that he wants you to do the leaving, so he doesn't have to face up to what he's been up to?
Do you think it's possible that you are still treating him as the man you thought he was - not the man that he has proved himself to be? Do you really want to fix things, really?
I totally understand the feeling that you don't want to chuck away all those years together, but really you deserve so much better than this. Your judgement is being clouded by the tragedy of what he is chucking away - but you can't change it by being more accommodating to him, or by "working it out". The truth is it's not working. IMO he sounds immature, and not at all committed to this relationship.
I mean could you even consider throwing away your relationship with your DD because she and your DP were a bit messy?! It's inconcevable isn't it?! He's either totally shallow (unlikely IMO) or making excuses.
You say " I have to know what I'm doing. I don't have that right now. It's so scary." Be gentle on yourself, it's early days. Your life has just been thrown upside down. You're doing all the right things IMO, you will get there. Like you said, one day at a time. Things will become clearer.
There is a future out there, past this bit, where you and DD are settled, happy, and you are genuinely glad you didn't waste any more of your life in this relationship. More than that - in this future, you are no longer defined by this relationship, you have moved on; other, more important things matter to you and make you happy.
It may seem like an impossibility now (it did to me back then) but it's not, it's yours for the taking. You just need to get through this bit first.
Sorry for the essay! I hope at least some of it is helpful.