AIBU waiting for an apology for saying he doesn't want to see me, it'll be like a holiday for him and so on, before contacting them again?
It's understandable for you to want an apology but really - what use would it be?
He won't mean it, just like he doesn't mean he's going NC with you.
People who are sufficiently dismayed by your behaviour to take the huge & upsetting decision to go NC don't ask you to come round anyway to cut their hair. 
You dad is a manipulative old git, & your mother enables him at your expense because it's easier for her - she's the one who has to live with his tantrums after all.
The best response you can give him is none.
Just drop the rope.
Then when he pulls on it - you won't be there, & he'll have to have an argument with himself instead.
I strongly advise you to stop contacting him, stop discussing him with your mum, & just crack on with your own life.
He won't let you get away that easily: he'll either contact you again to needle you for more drama, or he'll dispatch your mum as his Flying Monkey. And your mother will comply, just like she did this week -
and get 'secret' email from mother few hours before saying father is angry at me and I've hurt his feelings and just to apologise and not say anything more so he backs down and feels better.
Your dad got your mum to get you to ring him for the apology he demanded.
He put you through a command performance of 20 apologies.
He then made a contrary great meal out of refusing to accept the apology he'd demanded.
Can you see how he sets you up to fail?
How any apology, from either of you, cannot be genuine while he treats you as his personal Supply? queenbeeing.com/narcissistic-supply/
All that will happen if you insist on an apology is more drama.
All that will happen if you extract some grudigng & insincere words from him is that he will manufacture a new 'reason' to make himself offended so that he can place you back in the wrong & demand you apologise again. Just so he can reject you again.
It's a very tired old merry-go-round isn't it?
You have the freedom to stop all this bullshit - just by stepping lightly off the merry-go-round.
By dropping the rope.
By letting him "go NC" (ha!) with you, & not responding.
By using Grey Rock EVERY TIME you interact with him.
www.blunt-therapy.com/how-to-gray-rock-method-a-narcissist/
It will take some practice & willpower to change the way you interact with your emotional tyrant. But there is information & support out there, & I suspect you will find this site a tremendous source of help - outofthefog.website/toolbox-intro
You might also want to search MN for the "Stately Homes" threads, which are all about mutual support for adult children of .... let's just say "unreasonable" parents.
btw - the links I posted above are not about judging whether your dad is a narc or not: none of us can 'diagnose' & you don't need diagnosis. All you need is a set of techniques that help you manage the old git - you don't need to be wondering "WHY is he like this", you need to be concluding "this is HOW he behaves & this is HOW I can best respond to minimise the negative effect he has on me."
I'm sorry how hurtful & maddening your dad is. The more Grey Rock you practice, the better able you will be to choose not feel the pain he enjoys inflicting on you. Or at least feel it less deeply, & certainly be better equipped to deflect it & not engage with his nonsense. It will take a little time, but it is absolutely possible - reading the Stately Homes threads will show you how PP have been able to do just that. 