Can the Federal Government offer financial incentives to states to carry out policy that the Constitution prohibits at the Federal level?
Short answer: Yes, Congress can use the Spending Power to incentivize states to adopt policies that are Constitutional at the state level, but which Congress is unable to legislate on itself. It's been used to encourage states to adopt a legal drinking age of 21, so this could also include state prohibition of alcohol. (Moreover, Section 2 of the Twenty-First Amendment seems to guarantee to states the authority to regulate or prohibit the sale or consumption of alcohol within their territory, as they so choose).Longer answer: Congress may use the Spending Power to incentivize state policy formation within the parameters set out in South Carolina v. Dole (available here: FindLaw | Cases and Codes). There are four limitations:The policy incentivized must be rationally related to the type of spending being conditioned (i.e., conditioning federal highway funds on states adopting a minimum legal drinking age of 21 is OK).The requisite conditions sought from states needs to be unambiguous (i.e. Congress cannot ask states to meet some vague subjective standard, they have to set hard targets or terms).The policies sought must otherwise be constitutional for the states to enact (i.e., while Congress can condition federal spending on the adoption of a policy that exceeds Congress's direct regulatory powers, Congress cannot condition federal spending on the adoption of policy that "engage[s] in activities that would themselves be unconstitutional . . . [like] a grant of federal funds conditioned on invidiously discriminatory state action or the infliction of cruel and unusual punishment. (from Dole)."The conditions established by Congress cannot amount to coercion and states must be given a meaningful choice (i.e., the Supreme Court recently held that the Affordable Care Act's Medicaid expansion provision, wherein Congress gave states a financial incentive to expand their Medicaid coverage, "coerced" states by not granting them a meaningful choice because states couldn't reject the Medicaid expansion without relinquishing federal funds for their already existing Medicaid programs on which too many were already dependent.)Because Section Two of the Twenty-First Amendment grants states the authority to regulate or prohibit the sale or consumption of alcohol within their territory, the hypothetical program you suggest (encouraging states to reenact Prohibition ) could fall within these parameters depending on the kinds of federal funds Congress conditions. Highway funding and certain healthcare funds would probably suffice.