In the Tumultuous Thirties, the Spivakovsky Duo became the Trio with the addition of Edmund Kurtz, who had previously been personal cellist to the world-famous Russian prima ballerina Anna Pavlova. Kurtz had studied under Pablo Casals and Julius Klengel, respectively the finest cello exponent and teacher of the day, as well as the controversial Diran Alexanian, who had played chamber music with the immortals Johannes Brahms and Joseph Joachim.

Spivakovsky determined that to provide "as many variations of ourselves as mathematially possible," they would feature a vast repertoire of solo, duo and trio works. He also fearlessly decided to debut the trio in The Hague, due to its notoriety for unforgiving critics and demanding audiences. After five months of practising up to fourteen hours a day together, he deemed them ready for this severe test. From the review of their debut in Algemeen Handelsblad: "Debut extraordinary – of all the concerts that I have ever heard this was one of the most beautiful. Their solo as well as their ensemble playing is the most perfect that one can imagine." They toured the musical centres of Europe and leading critics proclaimed them the finest trio in the world, noting with surprise and delight the pianist's exceedingly rare ability to perform solo, duo and trio works to the highest standard.

The triumphant Trio returned to Berlin to find storm clouds gathering. Spivakovsky’s leading reputation for interpreting German composers had infuriated the Nazis, who were growing in power and began disrupting his concerts and attacking him in their press. When they put him on a hit-list, he was warned to get out of Germany by Strauss who penned him a coded message (a few bars of the first movement of the William Tell Overture, which signify an impending storm, followed by an exclamation mark). He hurriedly booked an Australasian tour of 70 concerts for the Trio and they boarded their ship a few days before Hitler was appointed Chancellor.

Australasian critics proclaimed them "the finest trio of instrumentalists in the world," "a revelation of the beauties of chamber music" and "supreme in the musical world today." Sought by the leading Australian music institutions, they joined faculty at the University of Melbourne, thereby avoiding being shipped back to Germany. However they found themselves required to run the gauntlet of the notoriously impossible “Dictation Test,” used by Australian immigration officers to immediately deport anyone they deemed racially undesirable. They also found themselves increasingly blocked from the international stage by anti-Jewish movements in Europe, forced to cancel their 1934 tour of Italy.

The situation in Europe quickly worsened and Spivakovsky received more and more requests for help from people desperate to escape Germany. He put his international career on hold and worked tirelessly to convince Depression-ravaged Australian employers to sponsor visas for these people. Meanwhile the careers of his Nazi-approved rivals flourished, bolstered by international tours and glowing press sponsored by Joseph Goebbels, Reich Minister for Propaganda and Public Enlightenment. In 1937 the Nazis proudly named Spivakovsky on a list of leading Jewish musicians "eliminated" from German culture, during their monumental cultural exhibition Gebt Mir Vier Jahre Zeit (named after the quote from a Hitler speech: "Give me four more years and you will not recognise Germany").

In 1938, Spivakovsky was relieved and delighted to finally become an Australian citizen and British subject. During the war years, he gave large patriotic and charity concerts and was appointed an Air Raid Warden due to his massive physical strength. At the end of the war, he was devastated to learn of the loss of his beloved younger brother Albert, who had remained in Germany to pursue his own promising career as a concert pianist. After a terrifying escape from Berlin, then dodging border guards and machine gun fire while carrying his wife through deep snow across the Swiss border, Albert had finally reached safety but succumbed to exposure.