Some people are beyond saving- there is nothing that you can say or do to get them to accept that their beliefs are wrong. So you're better off expending efforts on the option that disrupts the radicalization pipeline.
What could I possibly say or do to convince this person otherwise? They are so far beyond rational understanding of the vaccine that I'd rather take down the misinformation than be afraid of somehow re-enforcing that family member's beliefs.
I like to do in-depth research for myself (example: watching an entire Trump or Biden speech instead of relying on a selected soundbite), viewing the original video or source instead of blindly believing on what mainstream media says about them.
Unfortunately as more things get censored from social media/YouTube whether fairly or unfairly, it looks like I'll have to spend more time on "alternative" platforms, being exposed to the stuff that is common on such platforms. In the end, there's going to be the Twitter echo chamber, and the Gab echo chamber, etc (note that Parler seems to be dead).
A slightly more effective approach for you might have been to remove such videos from their recommendation algorithm. But, that doesn’t mean it’s ineffective for people who would be initially discovering this stuff.
Platforms, by their nature, are mostly worried about what's happening on their platforms - when it's occurring elsewhere, it is no longer their problem. It is a mistake to think YouTube wants to bring an end to all misinformation everywhere - their focus starts and ends with misinformation on YouTube. Balkanization is the best option they can hope for, as long as it's not on YT.
The arguments goes in both directions, if you don't handle it correctly then being too heavy handed has the opposite effect.
Pontius Pilate doesn't really care, as long as he's washed his hands of the matter and has rid of the man (and crowds) from his court.
But the pipeline is not a single thing. It’s a mutating and evolving entity. If you remove the content from one place, it shows up in another, but now it has more credibility because it’s been “removed for truth”.
Unless there is a plan to block these people from the internet entirely, disrupting the pipeline ends up being gasoline on a fire.
Such is the nature of a decentralized internet. The only centralized authority that can keep people off the internet is the government, and it would immediately run into freedom of speech issues (and I'm not a fan of government action. I'd much rather have private sites use their free speech/editorial powers to combat this).
Are many smaller fires better than fewer, but larger conflagrations? Depends on who you ask, I think so. However, platforms don't care about the larger picture, they are only concerned about the fires on their properties.
Then doing things on basis of motivating them is a dead end, and we should staunch the flow of falsehoods to keep other people from becoming contaminated.
I'd say that blocking the content doesn't always reinforce their beliefs. For a lot of people, reading something that is then blocked at a later date reinforces the belief that the information they consumed is not only true, but so true that it has to be censored by some authority, because it would threaten said authority's legitimacy.
As an example, imagine you think that the police are too violent, and you stumble upon police bodycam footage of a cop getting unnecessarily violent at a traffic stop. You bookmark the video, and then later when you try to tell people about it, the video has been taken down the police, for whatever reason. Wouldn't that reinforce your belief that police are too violent?
I know this isn't a perfect example, because a video of someone doing something is much different than an article making claims based on little to no evidence. But the reason some people's beliefs are reinforced by censorship is because they can't help but wonder if the people doing the censoring are trying to hide something.