Earlier quoted context omitted.
Refuse to ever see them in person again until they do. Block them from viewing your Facebook wall until they do. Open every phone conversation by asking them if they have done so, and to send you a photo of the certificate if they did, or otherwise politely but firmly end the conversation and hang up. If they show up to a family gathering, leave immediately and take your children with you. Ask them to send you a phot…
That's a great list of things to do if you want to feel self-righteous, but what do you do if you actually want to convince them?
No rational/logical argument basis would reliably succeed that I know of. People will surely try and no doubt some will succeed, but the argument approach is more likely to cause them to strengthen their anti-vaccination position than to change it.
The only way to reliably win is not to argue. Be clear that it matters to you, politely refuse to respond to barbs and baits, walk away rather than settle for their presence, deny them participation in your life, and ask them if their position has changed on a regular basis.
If you can construct a rational/logical argument method that is generally and widely effective, you can cure anti-vaxxers and anti-maxxers, and a whole lot of other societal ills. I support any such effort but after a couple decades I’ve gotten nowhere.