Fascism is, by most definitions, a form of authoritarian corporato-nationalism which emerged from the far right in Europe after the first world war, notably in Italy, Germany, and Spain, although there were also non-ruling Fascist parties in France and England. Your mother is probably confusing authoritarianism with Fascism; both Communist regimes (on the far left) and Fascist regimes (the far right) have been authoritarian in the past.

u/SunshineBag is an expert on Italian fascism and examined fascism through the lens of Football/Soccer in this episode of the AskHistorians Podcast, which might clarify what a Fascist regime looks like.

One thing to note is that Fascism is right-wing in the Traditional Left-Right Spectrum that emerged from the French Revolution. The Monarchists and Aristocrats sat on the Right side of the Assembly while the Revolutionists and Commoners sat on the Left side. The Fascism of Germany, Spain, and Italy align on the Right side because they all supported Monarchism/Imperialism to some extent. American political parties don't really fit into this context because neither the Left nor the Right associate with Monarchism or Revolution. Democrats are essentially Social Liberals or Egalitarian Liberals, while Republicans are Classical Liberals. Fascism was anti-Liberalism entirely.

The Fascists themselves rejected the label of Left or Right, and called themselves the Third Position, or Third Way, that was outside of the Left-Right Spectrum. It was both anti-Communist and anti-Capitalist. It rejected the Materialist worldview of the Marxists and also the Liberal worldview of the Capitalists. They instead embraced Corporatism and an Actualist worldview. This was basically a system where massive labor unions and massive organizations of capitalists managed the economy.

Corporatism is not Socialism, but it comes close to the positions many European Social Democrats had taken during and after WWI. From this perspective, Fascism was also close to the moderate Left in Europe but deeply opposed to the extreme Left and Bolshevism/Marxism.

With both of these points in mind: Yes, there were Left-wing Fascists within the Fascist movements but the overall Fascist movements were not strictly left-wing. So no, there were no left-Fascist governments.

The biggest point to make is that Fascism is not strictly Right or strictly Left. There were such things as Homosexual Nazis, Socialist Fascists, anarcho-Corporatists, Actualist-Communists, and so on, that existed within Fascist governments or within Fascist movements. Each one of these groups exerted influence to some degree.

Gabrielle d'Annunzio's Fiume expedition epitomizes most of these groups. D'Annunzio's group of nationalist followers seized a city that belonged to the Croatians and proclaimed it a regency of Italy. Alceste De Ambris, a anarcho-Syndicalist who supported Italy's entry in the war, helped d'Annunzio write a constitution that organized labor into national unions. They had the backing of Italian Arditi units and thousands of WWI veterans. D'Annunzio tried repeatedly to gain the support of the Italian Socialist Party but they had a deep hatred of De Ambris for his support of the war. At the same time, the Charter that D'Annunzio and De Ambris wrote allowed sexual freedom so homosexuality in Fiume flourished, even among the veterans.

You also see this cohesion of Left and Right forces in the pre-1930s Nazi Party and it didn't end until 1934 when Hitler purged the party and smashed the labor unions. For a short time before the Nazis seized power, homosexuality was seen as a product of nationalism and for a while homophobia was propagated by the Marxists to undermine Fascism. Meanwhile some Nazi labor unions like the NSBO were militant radicals who beat up factory owners who tried to cut wages. When the Nazis took power, the NSBO leaders believed the SS would begin rounding up and shooting reactionary factory owners. There was also the Strasserist wing of the Nazi Party that advocated radical policies. They were responsible for the 25-point program that advocated land reform, social security, nationalization of industries, profit sharing and the execution of exploiters. Joseph Goebbels actually joined the Nazi Party because the Strasserists were so far to the left. Goebbels was extremely sympathetic to communism and supported expropriating wealth from the aristocracy.

In 1934, Hitler and the Nazi Right orchestrated several purges that weakened and eliminated the leftist elements of the Nazi party. On May 2nd, Hitler began smashing independent labor unions and started reorganizing labor into the German Workers Front (DAF). For a short time, the NSBO was allowed to exist but then they too were purged and the remnants were integrated into the DAF. Hitler placed Robert Ley at the head of DAF. Ley was an industrial chemist for I.G. Farben, and really had no experience with labor policy. The Strasserists were also killed because they had become openly critical of the National Socialists refusal to implement socialism in Germany. Ernst Rohm was also very critical of Hitler's refusal to lead a socialist revolution. Himmler falsely informed Hitler that Rohm was orchestrating a coup against the Nazis. Rohm and the SA leadership were killed in June/July.

Mussolini's movement has similar associations with the Left but for the most part Mussolini refrained from purging his party. Mussolini himself was a former Marxist, and Michele Bianchi was a notable syndicalist before the war. There were also various intellectuals who participated in the government who had significant influence. Giovanni Gentile was a professor of philosophy who developed an Actualist worldview for Fascism. When the Fascists came to power, Mussolini gave Gentile several posts in the government, including a leadership position in the reform committee. The committee basically developed the Corporatist system for Italy and Gentile would go on to reform the education system as well. Ugo Spirito was also included and he had been a student of Gentile's Actualist philosphy. Spirito gradually developed the idea that Italy would have to evolve into a communist system and apparently (Spirito claims this in his autobiography) Mussolini agreed that Fascism could develop communism in Italy. You also had Nicola Bombacci, a Communist, who was early on a critic of Fascism and an active participant in the Third International that was meeting in Russia. In 1934, Bombacci embraced Fascism on the belief that Italy would develop communism before Russia. He remained loyal to Mussolini and the RSI after 1943, and was eventually shot and hung alongside Mussolini and Clara Petacci.

Recommended books:

• Mussolini's Italy - R. J. B. Bosworth

• Gabriele d'Annunzio - Lucy Hughes-Hallett

• The Rise and Fall of the Third Reich - William L. Shirer