Trump is preparing to go nuclear on our allies if they don't toe the line on our stupid and unilateral decision regarding Iran.

President Donald Trump threatened "severe consequences" for those who continue to trade with Iran, as administration officials said Monday that newly re-imposed US sanctions are meant to change the regime's behavior, not topple leaders in Tehran.
"The United States is fully committed to enforcing all of our sanctions, and we will work closely with nations conducting business with Iran to ensure complete compliance. Individuals or entities that fail to wind down activities with Iran risk severe consequences," Trump said in a statement about penalties that will go back into effect at 12:01am Tuesday.
A senior administration official said that, "our stated policy has not been regime change, it's been to modify the Iranian regime's behavior."

There's two bullsh*t statements here: a) We aren't "working closely" with anyone. We are just imposing our will like a bully, and b) We obviously want regime change.

In response, our European allies are trying to grow some guts.

The EU will allow European companies hit by new US sanctions on Iran to sue the American government amid concerns Brussels cannot provide adequate protection for companies operating in Tehran.
Under a “blocking statute” first drawn up by the EU in the 1990s, European businesses will not have to comply with the US’s secondary sanctions designed to hit Iranian cars, gold and other metals as of August 7. EU companies hurt by the sanctions can also take the US to court in EU member states for compensation.

It's unlikely that the EU measures will be able to shield these companies, but it is very likely that this will trigger legal challenges and cause a diplomatic break.
It's also expected to cause oil prices to spike above $90, which will probably trigger a recession.

The largest buyer of Iranian oil, China, will flat out ignore our sanctions threat and keep buying.
They key is the second largest buyer of Iranian oil, India. Their plan is a bit more ambiguous.

What government has said: Foreign Minister Sushma Swaraj at first stated that India only complied with United Nations-mandated sanctions. Then, in June, the oil ministry held a meeting with refiners and asked them to prepare for a scenario of ‘drastic or zero’ imports of Iranian oil from November, Reuters reported. The country is currently trying to find alternative payment methods to enable it to continue buying from the Islamic Republic.

These secondary sanctions are the only way that Washington's unilateral sanctions will have any bite. Despite our being the largest economy in the world, the U.S. does very little direct business with Iran.

A landmark study published in the 1990s by the Peterson Institute for International Economics found that unilateral US sanctions achieved their foreign policy goals only 13% of the time .

The rare instances when unilateral sanctions work involve countries that have extensive trade relations with the US, clearly not the case with Russia or Iran . Russia is low on the list of US trading partners, and Iran has had virtually no economic or commercial relations with the US. Neither country is dependent on US trade or likely to submit to American economic pressure.

There are two dangers from the Iran sanctions.
One problem is that overusing sanctions (and imposing sanctions on many of your allies is de facto evidence you are overusing them) comes with a cost.

Sanctions work because they cut targets off from dealing with U.S. citizens and American financial institutions—a complete severance from the world’s largest economy and its most important financial center. If Washington used this power idly, Lew suggested, it could encourage countries to find partners outside of the United States, and undermine sanctions’ deterrent effect.

Both the executive and legislative branches seem to have ignored Lew.
...At their most effective, sanctions are the product of multilateral efforts to solve clearly articulated, shared global-security concerns. Now they are becoming strident expressions of displeasure from an isolated United States, often wielded in service of domestic partisan priorities—a careless approach that may well neutralize the effectiveness of these powerful tools.

The other danger is deadly serious.

To Iranian President Rouhani: NEVER, EVER THREATEN THE UNITED STATES AGAIN OR YOU WILL SUFFER CONSEQUENCES THE LIKES OF WHICH FEW THROUGHOUT HISTORY HAVE EVER SUFFERED BEFORE. WE ARE NO LONGER A COUNTRY THAT WILL STAND FOR YOUR DEMENTED WORDS OF VIOLENCE & DEATH. BE CAUTIOUS!

— Donald J. Trump (@realDonaldTrump) July 23, 2018

Iran said its Islamic Revolutionary Guard Corps held a naval exercise in the Strait of Hormuz last week "within the framework of their annual training program."
The exercise was held with aim of "controlling and maintaining the security of the international waterway of the Persian Gulf and the Strait of Hormuz, and to proportionately counter any threats by the enemy," semiofficial Tasnim news agency reported.

If Trump actually succeeds in cutting off Iran's oil buyers, then Iran may feel it has no choice but to shut off the Straight of Hormuz.
This would trigger a war, and the U.S. would have very few allies in this war except for Israel and Saudi Arabia. Even if that war could be won (a very big "if"), it would come with baggage.

The only military action that can truly prevent Iran from acquiring a nuclear weapon, then, is for the United States to invade and occupy the country, potentially turning it over to a U.S.-friendly regime that would uphold Iran’s non-nuclear status. Despite the widespread support in the United States for preventing Iran from building a nuclear weapon, this option is almost never proposed by any serious observer.
Part of this undoubtedly reflects America’s fatigue following the wars in Iraq and Afghanistan. However, it goes much deeper than that—namely, while Iran’s military is greatly inferior to the U.S. armed forces, the U.S. military would not be able to conquer Iran swiftly and cheaply like it did in Iraq and Afghanistan. In fact, Tehran would be able to impose prohibitive costs against the U.S. military, even before the difficult occupation began.