That's not how it works! First of all, neither Arizona nor the Executive branch can amend the federal constitution by themselves, they can't even force the Congress to look into the matter unless enough states ask for it (some 34 are needed) and even then it is up to congress if they want to take matters into their own hands. If the congress does not want to do it, they could just call a meeting to discuss the matter, then vote to drop it and there is no way to force the matter. Even getting enough states together isn't an out as congress still needs to decide to delegate.
It is entirely upon Congress to decide if they want to discuss and write any proposed amendment - or to call the convention. Anything other parties (press, executive, states) say is at best a suggestion to the congressmen and can be entirely disregarded if it acts on its own, and it is only up to Congress to call the convention under Article V - but no timeframe is given! They could very well sit on the matter for a few years, even as they are obligated to call it eventually.
The Congress, whenever two-thirds of both houses shall deem it necessary, shall propose amendments to this Constitution, or, on the application of the legislatures of two thirds of the several states, shall call a convention for proposing amendments, which, in either case, shall be valid to all intents and purposes, as part of this Constitution, when ratified by the legislatures of three fourths of the several states, or by conventions in three fourths thereof, as the one or the other mode of ratification may be proposed by the Congress; provided that no amendment which may be made prior to the year one thousand eight hundred and eight shall in any manner affect the first and fourth clauses in the ninth section of the first article; and that no state, without its consent, shall be deprived of its equal suffrage in the Senate.
Then it is upon every single state to ratify the amendment, and if less then 3/4 sign it, then it is not in force yet. It took 202 years to ratify the 27th amendment, which was brought up together with the first amendment! Nowadays, amendments come with a date if by which they are not ratified, they are tossed.
However, any state can alter its state constitution under its own rules. But they can't have stanzas in their constitution that breach the federal constitution.
but... Convention under Article V?!
In the past, the Convention has never been called upon. To make congress call for it, you need to pass a lot of thresholds:
- first, the government is usually seen as the executive branch of each state, which just plain can't do anything beyond asking its own legislative body to sign an application to ask for an amendment. Let's assume he wants to get the repealed amendment back.
- Now, we have a bill in the state legislative body, which then might be approved. Let's assume Arizona might be the first, but what now? We only have one single request to congress! One vote for Prohibition.
- Now, it needs 33 other states to petition for a convention that matches what Arizona wrote. If 32 want the same and one wants Prohibition and ALSO gambling ban in the same? It's possible that that might be seen as different items and thus different reasons for a convention, but that is untested as it never happened.
- Now, let's assume we get the needed 34 requests. Now it is up to Congress to call the convention...
As noted, Article V conventions are totally untested, timeframes are not given in any relevant law and it is even unclear if the Supreme Court could force Congress to call a convention if it would just not do so on its own. The problem of enforceability by the courts is because of Coleman v. Miller (307 U.S. 433) - it's a political question and the Supreme Court has repeatedly held that it shall not interfere in Political Questions.
