He's bad news, expecting you to justify your decision to meet up with that relative on that night.
Can you see how you already changed your behaviour three times?
Firstly you justified it to him, when no justification was necessary. You made a decision and he should have accepted it without question or comment (except, "have a nice time" or similar and arranging when else he could meet you that week).
Secondly, you invited him along on a girls night out! The very definition of which means he's not invited! If you've read the thread you'll see from others that contrary to what you told him, he's not welcome on a girls night out.
When he's free isn't your problem, if he wants more 1-2-1 time with you, let him change his life to achieve it instead of creating a situation in his life where he's limited to one available day and you're expected to toe the line and comply because he decrees it so.
He's also shown massive escalation in controlling behaviour already. Going from moaning a bit (WTF?! Like he has any right to do that!) over a few weeks (so repeatedly hassling you about your perfectly reasonable choices, aka bullying you) to getting angry the second time, after moaning at you the first time didn't work to make you never do it again.
He's done you a favour, if the escalation was slower you might not have picked up on it so soon. That feeling of awkward, of something not being quite right, that's the feeling of someone trampling over your boundaries. People who do that are never good news.
So onto the third way you've changed your behaviour. He's tying your thoughts up (and your spare time) with justifications, explanations, attempts to reason with him, attempts to make him see/understand your point of view, defending your choices and views. You're spending more time trying to understand him, figure out why he's like this so you can counteract it to him with logic, questioning yourself if you're the unreasonable one, questioning what's normal. All in the hope that if you say the right thing he'll suddenly understand and therefore stop his comments. He won't, because these types of people already understand, they just don't like it so they try to manipulate to get a situation they do like. It's not ignorance on his part, it's deliberate. It's a change of behaviour because I bet date one with him wasn't like this. I bet you don't behave this way with others in your life (and if you do, they're toxic too).
DARVO means Deny Abuse and Reverse Victim and Offender. So he tells you his actions are normal and it's not him that's unreasonable, it's you and you're the unfair abusive one. That's what he's doing, except this time he blamed your relative not you, but yes sort of still blaming you for not challenging your "rude" relatives behaviour. The relative wasn't rude at all for asking you on a night out on any day of the week.
Don't JADE means don't Justify, Argue, Defend or Explain. It's how to deal with arseholes. You inform them and that's it. End of. Nothing else. Don't get sucked in wasting your time telling him why you have the right to make your own decisions. He already knows, he just doesn't like it.