You have no idea the magnitude of the can of worms you are opening there. More like a wormhole that links to a series of universes completely filled with worms. Giant space worms with nasty sharp pointy teeth.
You are correct that unvaccinated people should live in isolation from others, but that clashes with your claim that the government should be able to force people to get vaccinated.
A better solution would be to leave it up to state or local governments to come up with such laws, perhaps based on recommendations from the Feds. Then there will almost certainly be some non-vaccine area that people can go who don't want vaccinations, and vaccine mandatory places where people can go to be safe from those diseases. Eventually, those places that allow non-vaccination will experience the higher costs and increased mortality that comes with that, and people will come to their senses or die out (or it turns out to not be that big a deal and vax-mandatory places abandon the checkpoints as they are too expensive to maintain).
In practice that would be hard to implement, though, as it would require internal checkpoints. Really this is all pretty Orwellian no matter how you look at it.