If this is the New Norm, and vaccinations are going to be mandatory (or/and testing…the doctor did say "or tested once or twice a week"); then the answer isn't forcing the vaxx, but updating healthcare to embrace both vaccinations and testing as being PAID FOR through a person's INSURANCE.
Or, just pass MEDICARE FOR ALL and be done with it; that way if you choose for you and your family not to take the jab, you then can get tested as required and it will be paid for.