OK, so for a living I talk on the phone to complete strangers and make them do my bidding. To train you in what I do would take forever, but it amounts to manipulation, and it is not for the faint of heart.
I'm sorry you're in this position. If my Stepson were still living with my ex, and he is exactly your age, I'm pretty sure one of them would kill the other, and my ex sounds a lot like your dad. My hat's off to you. (And my money's on my ex - my Stepson has the softer heart, just if you were curious.)
First off, if you live in someone's house, you do so by their rules, regardless of what constrains you to the home, how many problems are involved in moving etc. ad nauseaum. If you live with an OCD control freak with a temper, a personality disorder, and a reality perception issue, then you live by THOSE rules. It sucks, but there it is.
So... is it a rule you have to work or just parental pressure to make all decisions the way they wish it? If it is a rule, what are the arrangements for paid vacation days? It's important to think this out logically and like an adult -- this is what your Dad likely is really looking for, not so much the attendence at work, but the adult decision-making process. If that's not what he's looking for, it's important to be smarter, more devious, and find the loophole.
Next, whenever you say "no" say two positives, the negative then the positive. E.G. "Dad, I know this is important to you, and I want you to be proud of me. Unfortunately, what you're asking just doesn't work out. I do appreciate the input.
Then, address his concern: "I know you want me to be responsible and I appreciate the advice. It felt a little weird to be in this position to me, too. I thought the best thing to do was to notify my employer right away. They offered a solution that works well for them. See, if I take a bus that early, they fully expect that I would arrive to work tired and be less productive on their time. They'd really rather I was less productive on my own time, and in their view that is what my paid vacation days are for. I get, as a result of this, one fewer paid vacation days. However, if I do as they ask, my shift is covered and there is no hardship to my employer. Additionally, it would not be possible for me to make a habit of this. Really, while I do understand why, I need to make sure you understand that you and Mom are the only ones having a problem with this. I don't want to disappoint you, but since my responsibility to my job appears to be your primary concern, and it certainly is mine, I also want to make you aware of their bias. I will see you later today and I love you and thanks for looking out for me."
Follow up statements to be used as needed. "I understand what you're saying. This is just what I need to do for me." "I think if I were in your shoes, I'd feel really (frustrated/angry/disappointed/whatever) right now." "That must be (aggravating/frustrating, dissapointing/whatever)." "I'm really sorry you feel that way." "It was never my intention to cause you distress." "I know you love me and want what's best for me. Sooner or later, I do have to learn to handle these things on my own -- you can't be there for me forever." "I'm sorry, I just don't see it that way."
Listen! Don't sit there and mouth words at the phone while your Dad rants. Listen to understand. This is a sort of "know your enemy" thing. If you know what his issue is, you can use it to bend him to your will.
Communication style -- match his. Does he talk about feelings? (They're going to think you're flakey. They're not going to trust you) Then talk about feelings (They appreciate my calling so promptly and prefer this approach) Does he talk about facts and things and stuff (A job is a job and you go to work when you're expected and you do your job)? Well then, you give him facts (my job comes with paid vacation which they expect me to use at times like this). Is he direct and short? Be direct and short. Is he all wordy? Throw more words and details at him. Does he tell you he's looking for your respect? Just tell him he's got it. Does he throw Mom on the phone when he doesn't get his way? The second she's on the phone, match her in the exact same fashion. Does he switch styles and focus part way through the conversation? Switch with him.
Posture: Be proactive and perky. Yeah, I know, but try it. Flip the negative statements on end to be positive. For example, instead of "I can't be there until two" try "No problem -- I can be there at two." If they say something you can twist, or that you intend to do, start off with "Absolutely! That's why I ..." So, as an example, if Dad says your responsibilty to your job is paramount, you pop in with an enthusiastic agreement, and that's why you called them right away and put them in the driver's seat. You'll need an agile mind for this conversation. You want to find as many ways to tell him he's right as you can, followed by 'evidence' that you have done precisely what he suggested, just not the way he's suggesting it.
If all else fails, go with "You're right, Dad. I'm sorry and it won't happen again." Oh, hey, in fact, in keeping with that, you might try beating yourself up. If he's likely to defend you. "I suck. I know I suck. I can't believe I'm in this position. I feel like a total failure. I'm sure as heck not going to do anything different than what my work asked since I got in this position. This is so stupid! How are people supposed to hold down jobs when this kind of crap happens. I'm scared -- I don't want them to hate me...." Blah blah blah.
Good luck. Sorry you're at odds with your Dad.