In your hypothetical scenario, if vampires were to somehow gain control of the government, could they simply pass a law stating all vampires are invited in all domiciles?

Yes, but it wouldn’t have the effect you expected because the people still living on those homes have not invited them in.

Invitations are not associative and not transitive. If I invite John to my enter house, that doesn’t allow James to “infer” that he’s also invited, nor does it allow John to invite James into my house.