First of all, as you know, your dad’s wrong. If he took off driving for an extended period of time, and started up again, yes, it would come flooding back to him, because he has decades of experience to draw back on. You don’t have that.
What’s very hard is developing judgment, and you have to get that through practice, and you’re going to make mistakes. What’s terrifying for the parental driving instructor (and yup, I’m one), is that both of you could die from this development of judgment.
It’s stressful for you, but yes, it’s also incredibly stressful for your dad, too. That doesn’t mean he has the right to make you feel incompetent, though. Yes, you will get it – it’s just going to take a while, and starting and stopping at practicing doesn’t help.
If you really feel like you’re starting over again, I suggest you practice, not in a car park (“parking lot” in USA-ian) as BloodRedThorn suggests, but…this sounds a little crazy – in a cemetery. First, there’s usually not a lot of traffic in a cemetery, like there is in a parking lot. And you can drive as slowly as you like in a cemetery and no one will honk at you or try to get you to speed up through tailgating. They’ll just think you’re mourning. There’s lots of opportunities to practice turning and going round and round. Plus, if you do hit something major and you die, they can just roll you into a grave right there.
Kidding. Just kidding.
Then, any time you go anywhere, assume you’re the driver. Don’t spring it on people, because they may not have put it in their schedules that you’re driving, and probably it’ll take you longer than if an experienced driver was driving. So, you know your dad needs to go to the hardware store. Declare it early – “Dad, I know you’re going to the hardware store. I’m driving, OK? When do you think we should leave?”
This way, you’ve made the assumption – of course you’re driving! You’re just confirming it with him. This gives him time to go, “Ok, sure, I’ll let Lou drive” – gives some time for parental emotional and mental preparation.