If LW actually has paperwork that says they can make medical decisions for the kid, they might legally get away with one vaccination (although I still think most doctors would say, "this baby is not my patient and I don't know their history so I won't vaccinate them") but then the parents will revoke the paperwork and the kid will have a very incomplete vaccine series. And of course I am not a lawyer -- I'm coming at this from my time in medical admin and reading charts.