How do I psychologically change someones mind?

What do you want to say? What do you not want to say?

I want to show that it means so much for him to be there, and that it is an important occasion and not something small that he can flake on. But I know I can guide his thoughts if I tried hard enough, I just can't think of words/sentences to do so.

I know I shouldn't say that he's expected to be there, purely because it means I'm demanding him to go when that will only push him away

So asking without sounding demanding? You don't want to force him, but you also want him there?

'It's really important to me and I would really appreciate it if you could come'

Exactly that! But I fear that saying that won't be enough

Dear, if that's not enough to convince him of the gravity, I have three words for him.

'you are dumped'

You condition them to that behaviour you want. Research Pavlovs dogs

I don't think it's the same principle, I've learnt about Pavlovs research, and it's harder than just praising them if they decide to come.
It's that process of getting them to decide to come themselves without me telling them they should be there. It's hard to explain hope that makes sense haha.

If only it was that simple it's actually a family member

Oh right... so you need their mind to change and agree out of the blue? You need a magic wand hun haha

Family members can be dumped to, being a relative is not an excuse to mistreat you.