There does not appear to be any records of the use of poisonous gas on Iwo Jima, but the proposal was entertained before the battle, as Iwo Jima is a small island often subject to strong ocean winds which would blow away any gas fumes before American troops arrived. Admiral Chester W. Nimitz, the commander of the U.S. Navy’s Pacific Fleet, proposed first jamming any Japanese communications from the island so officials on the Home Islands would not know that gas was used against their troops (at the time, both Japan and the United States were among the several countries that signed, but were not officially party to, the 1925 Geneva Protocol restricting the use of biological and chemical weapons in warfare), and then saturating it with gas before the landings. Another recommendation was changing the color bands and markings on naval gas shells so that sailors would not know they were firing gas. The plan was accepted at every level, but President Franklin D. Roosevelt denied it as it did not conform to U.S. policy on the use of gas. After the battle, Nimitz was regretful that gas was not used, probably because of the high number of U.S. casualties. Other backup plans were prepared for an early 1945 campaign in the Pacific, including bypassing Iwo Jima for a less-defended island, or using an atomic bomb on a Japanese-held island if or when one became available.

As the Pacific campaign wore on and American casualties grew steadily, the use of gas was proposed against Japanese-held islands, principally those where few or no civilians, and only Japanese soldiers (such as Iwo Jima), were present. The Lethbridge Report, originally produced in 1944 by a British Major General John Sidney Lethbridge, outlined how gas could best be used in tropical conditions like those found in southwest Asia or the southwest and central Pacific. Further developments were made top secret and turned over to the Office of Strategic Services, the predecessor of the CIA.

U.S. policy towards the use of chemical and biological weapons during World War II was purely retaliatory, in that enemy forces would need to use them on U.S. troops first. President Roosevelt was vehemently opposed to the use of any chemical or biological weapons in a first strike, as were members of his staff;

He [Admiral William D. Leahy] advised the President that using gas or germ warfare 'would violate every Christian ethic I have ever heard of and all of the known laws of war. The reaction can be foretold: If we use it, the enemy will use it.'

The U.S. did maintain emergency stockpiles of gas within theaters of operations in case that situation came to pass, however.

U.S. Army Chief of Staff George C. Marshall proposed using gas against Japanese targets after the heavy losses on Iwo Jima, where total American casualties actually exceeded those of the Japanese. He only mentioned its effectiveness in military terms, and used the term "gas" and not "poison gas;" he hoped that the use of gas against Japanese military forces (who were equipped with gas countermeasures) would urge any civilians to evacuate or move away from the battle zone. Marshall had tangential experience with gas during World War I, and presumably knew that certain types often caused severe suffering to those so affected.

Your wife may be thinking of the widespread use of white phosphorus, a pyrophoric (self-igniting) incendiary agent which burns at about 5,000 degrees Fahrenheit and produces a thick, choking white smoke. In World War II, white phosphorus was used as an antipersonnel and antimateriel weapon, in hand and rifle grenades, artillery and naval shells, and aircraft bombs. It could also be used as an obscurant to mask troop movements or as a target marker, but there was a non-injurious smoke, hexachloroethane, that was more suited to that particular purpose. Chunks of white phosphorus can cause severe burns if they contact human flesh, and will only stop their action when used up or removed. Too much elemental phosphorus ingested or absorbed into body tissues can lead to phosphorus poisoning, characterized by nausea, vomiting, diarrhea, an odor of garlic on the breath, and eventual kidney and liver failure. Chronic exposure to white phosphorus vapors, like what was encountered in the match-making industry during the 19th century, can also cause “phossy jaw,” a condition in which easily exposed bone such as the jawbone becomes necrotic.

In 1980, the United Nations Convention on Certain Conventional Weapons was signed by over 120 countries at Geneva, Switzerland. Protocol III of the treaty restricts the use of incendiary weapons (including white phosphorus) against civilians, or in areas where legitimate military targets may be close to civilians.

Sources:

Alexander, Joseph H. Closing In: Marines in the Seizure of Iwo Jima. Washington: Marine Corps Historical Center, 1994.

Newcomb, Richard F. Iwo Jima: The Dramatic Account of the Epic Battle That Turned the Tide of World War II. New York: Henry Holt and Company, 2002.

Settle, Frank A. General George C. Marshall and the Atomic Bomb. Santa Barbara: Praeger, 2016.

Spiers, Edward M. Chemical Warfare. Basingstoke: Palgrave MacMillan, 1986.

Sprietsma, Charles F. Analysis of the Battle of Iwo Jima. Montgomery: Air Command and Staff College, 1984.

The US did not use poison gas on Iwo Jima. While there may have been plans to use mustard gas for the planned invasion of mainland Japan they were never enacted. There was also a certain fear of retaliatory deployment of chemical weapons on both sides: while the Japanese used chemical weapons on multiple occasions in their invasion of China they did not deploy them against the Allies partly because they feared that the superior industrial capabilities of the Allies would lead to a chemical escalation that would not be beneficial to anyone.

I do seem to recall the Japanese Yushukan military museum to have pushed some kind of narrative like this for their Iwo Jima exhibit at one point. However the Yushukan military museum (located at Yasukuni Shrine) is rather infamous for being extremely right-wing and extremely revisionist in their exhibits, much more so than most other Japanese museums. For instance I recall an exhibit which stated that "Japan had always wanted a strong and independent Korea, so they annexed them." It is quite possible that your wife may have heard this allegation through similar sources.

While poison gas was almost certainly not used on Iwo Jima, Max Hastings states in his book Retribution: The Battle for Japan 1944 - 45 that tear gas was used.

The gas was used in an attempt to flush out Japanese soldiers from caves during "mopping up" operations. According to him it didn't work, and a flaming slurry of salt water, gasoline and oil wound up being used instead.

Having said this, I am unable to find any other source for the claim that doesn't point back to the book.

That doesn't mean there isn't any... I would be frankly astonished if Hastings made it up out of whole cloth... it just means that I can't find one. My copy of the book is on loan, so I can't reference his source list either. I'm certainly disposed to assume he knows of which he speaks.