There's not really much to say beyond the fact that the King of Italy remained the head of state throughout the fascist ventennium. In fact, it was the King of Italy who gave Mussolini his mandate to form a government after the March on Rome in 1922. I had expanded on the specific mechanism through which Mussolini rose to power in an answer that might interest you here.

The King's role as head of state, although certainly much diminished in the midst of the cult of personality around the Duce, nonetheless carried important political and institutional influence; all through the dictatorship, Mussolini and the Monarch held a weekly meeting each Monday, as was the custom for Italian Prime Ministers. Mussilini and King Victor Emmanuel certainly had a working relationship, however together with Catholicism and the Vatican, the monarchy and the people's loyalty to the monarchy was one of the things which worked against Mussolini's grip on the country. This answer by u/Klesk_vs_Xaero goes into a lot of detail about Mussolini's gradual rise to power, and although not specifically about the monarchy's relationship with the dictator, you will see how the monarchy and monarchist's reaction to fascism was a continuous, and important, current all thought the ventennium.

As the war in Africa took a nosedive and Anglo-American forces began planning to disembark in Sicily, members of both the military leadership and fascist establishment began a multitude of plots to unseat Mussolini; many saw the king as a vital ally. When the Great Council of Fascism voted to remove Mussolini in July of 1943, they did so by voting to hand over executive power to the monarch.

The monarch had indeed also grown weary of the dictator, and had for weeks discreetly lent an ear to proposals for a post-Mussolini Italy. Nonetheless, the King was slow to respond to these plans and did not himself participate in any scheming, in spite of public opinion which, having grown disenchanted with the fascist regime, was becoming increasingly disappointed in the King's lack of action. However, the King's institutional role had remained intact over the course the ventennium: it was still he who appointed the head of government. The day after the Great Council of Fascism's meeting, the King received Mussolini, who communicated the result of the Council's vote. King Victor Emmanuel consequentially removed Mussolini as head of government, appointing in his place General Pietro Badoglio. Mussolini was himself subjected to a somewhat convoluted arrest, having been apprehended on his exit of the King's residence with the explanation that his own safety was in danger from angry mobs. Loaded onto a military ambulance, Mussolini was held at the Officer Cadet School. It is unclear when he was told or realized he was under arrest, however he must have gathered as much when he was taken to the Island of Ponza, ironically the predetermined destination for anti-fascist exiles. This would be the first of many locations where he was held until sprung from prison by German forces in September.

The King and the new government headed by Badoglio, on the other hand, signed an armistice with the Allies and now faced with an imminent german occupation fled to Brindisi, in southern Italy. Mussolini, on the other hand, after being sprung from detention was placed at the head of a puppet state in the north. Italy was effectively split in half, and would remain so until Mussolini's assassination and the end of the war.