AIBU to not know how to deal with this kind of person?

You have to learn to pick your battles I think and only go in on the things that are actually effecting you. The rest of it let it flow over you and be able to laugh about it afterwards. This actually sounds not dissimilar to having a teenager who always thinks they know best.

It's decisions affecting the care of an elderly relative

It doesnt matter- presumably they are an adult and dont have dementia which puts them at risk, in which case they can make their own decisions- doesnt mean you have to get into disagreements or arguments with them about it. If they get angry, let them get angry.

Just because someone is older doesnt mean you have to do whatever they say.

Is this a male relative? Anyway, an adult like that is not going to change, so just stop playing the game, don’t offer any help at all, even if they ask for it say “I don’t know”. In other situations the mumsnet classic “no is a complete sentence” might actually apply for once. It’s clear they don’t actually want any help or advice from you, so stop helping/advising.

So bloody what? let them huff and puff- the world isnt going to stop turning on its axis just because they choose to have a strop. They cant have an argument with you if you refuse to engage in it.

I feel like you're just shooting down every suggestion we make. There is no magical miracle phrase here that will change this person - you either put with it, or put boundaries in place.

Also, I dont understand how this person's decisions are affecting your life so much if you are low contact with them already...

Huffing and sulking isn't an argument though, right? You don't have to care or react or even act like you've noticed. It's like tantrums in kids - if you teach them that they can get their way by doing it, they keep doing it. Nothing will ever change if you reward daft behaviour.

With the screwdriver thing, I'd just start using the screwdriver in my hand to do whatever it is, while they're rummaging.

With the other things, I'd get up and go home. If they queried why later, I'd tell them it didn't seem like they were listening to anything I said, so I thought they wouldn't miss me.

You need much better boundaries. You need to stop taking it personally and you need to stop agreeing to things you don’t want to.

Yes, it’s wildly infuriating. But you know what they’re like and you can’t change them, only your reactions to them.

If it involves your children or something you have control over just use the broken record technique "No, that is not a good idea due to xyz", if they then say "live a little!- come on!" repeat again, and again and again and again. Dont alter the phrase in any way, just keep repeating it and keep the emotional temperature low and calm but do not back down. Imagine an iron fist in a velvet glove.

Dont get upset or angry but be firm, polite, and unrelenting.

The only one of the three scenarios you list that affects you is the taking the children to the park one, and assuming they’re your children, you just do whatever you’ve decided.

Sure, I can see it’s irritating. But maybe they find you telling them what to do irritating too.

Simple- stop giving them advice. When they say they want to do XYZ just say "sounds great". The issue here is that they arent listening to you and think they know it all anyway so let THEM research it, they arent listening to your opinion anyway so you're just screaming into the void! You may as well be talking to the cat.

Even better if they go full on into something and it turns out to be shit. Sometimes its the only way people like this will learn.

I know people like that - it's incredibly irritating.

I wait until they expound their great idea (that I've already told them) and then say, "Oh yes, great idea!" Or "Fancy that, who would have thought it?"

Yes.

Or they are looking for something that I know isn’t where they think it is but they will still empty the entire thing out to find that it is in fact not there just as I told them, it’s not fucking there.

or, can’t have a civilised conversation about nothing in particular because they are extremely opinionated, never wrong and will not be told anything other than their own views.

They feel it their duty to tell people their opinions because they are “straight talking”.

Yes OP, I feel your pain.