Actually, Persano wasn't popular at all with the King, who held a grudge against him because he was convinced that Persano had willingly grounded the royal yacht on the coast of Sardegna.
They kept him simply because there wasn't anyone else; his subordinates were junior and were no better than him, his captains, while personally brave, were not prepared to make the jump between sail warships and steam warships, and performed understandably poorly (the captain of the Re d'Italia, Captain Fàa di Bruno, was glorified as having killed himself when the ship was sinking, but it appears that in fact he jumped for it but couldn't swim far enough and was dragged down with it).
I did not know about the incident with the royal yacht, but it does not change the picture. Persano was kept in his place - notwithstanding his attempts to resign - because he was a Piedmontese count, and as such part of the establishment. However his correspondence during the crucial period of 1866 is an unmitigated collection of whinings, accusations and complaints.
Tegetthoff was sent to Istria at the beginning of the war, and the situation of the Austrian fleet (which had been neglected after the departure of Maximillian for Mexico, was quite poor. However, rather than complaining like Persano did, he applied himself to training as much as possible the fleet.
Persano did not apply to training - which was what the Italians were missing: there ships were much more modern and with better guns than the Austrian ones. All over the course of the war, Persano never appeared to have a strategy in mind, nor did he show any appetite for pro-active actions, which is a cardinal sin in an admiral. When the government forced him into action after Custoza, he went for Lissa but without any strong feeling about it. It looks like that he picked up at face value the suggestion which the Minister of Navy, Depretis, sent him in a scathing letter: "...we have done nothing better than to put together a squadron that dares not meet the Austrians? .... If Tegetthoff dares not meeting us, we will effect a landing somewhere on the coast: at Lissa for instance. Lissa, by its central position, would ensure us the sovereignity of the Adriatic; let us take Lissa." It does not appear a positive order to attack Lissa, but rather the order to do something. The admiral of the Italian fleet who could not make a plan on his own took it at face value, and bungled its execution (the telegraph cable was not cut and the island was invested in different places, rather than concentrating all efforts against Porto San Giorgio). The result was that when he got news of Tegetthoff imminent arrival he was still engaged in reducing the Austrian forts and had to reimbark the troops and prepare for action. Not that he had a lot of ideas here too: he ordered the fleet on line, but left too wide a gap between the first squadron and the rest of the fleet, then he changed ships without signalling his division commanders, with the result that everyone was looking at the Re d'italia for admiral orders, while the admiral itself was esconced on the Affondatore. The battle was confused, and there were a number of opportunities to gain the upper hand, but it did not came to pass. Persano was tried in the Italian senate after the war: he was found not guilty of cowardice but convicted of negligence, and the verdict is probably a correct one. Still Persano wasted a magnificent opportunity (a positive outcome at Lissa would have left all the Adriatic under Italian control) and Tegetthoff took a crazy risk and won. Whatever the previous record of his divisional commanders was, I doubt that either Albini or Vacca could have performed worse than he did: an English historian compared him to John Byng, the English admiral shot after a court martial over the loss of Minorca "pour encourager les autres". Maybe a similar outcome for Persano would have done wonders to encourage the others.
As for the Italianization, I say that it's going to be just a little bit less harsh than in OTL; no vandalization of the Narodni Dom, no fascist beating the hell out of Slavs. But it's not likely that they are going to take it easy; in the renewed nationalistic sentiment, they are going to be tough on Germans and Slavs. Perhaps they'll let them have elementary school in 'other languages', but secondary and university are going to be compulsory Italian. Of course, no statue for Walther Von Der Vogelweide in Bolzano, but plenty of statues of Dante, Columbus, Francesco Morosini and Enrico Dandolo and others like them.
Once again: it is 1866, smack in the age of nationalism. One cannot look at events of that time from the perch of a 21st century political correctness.
I would be surprised if a successful Italy would not make much of the heritage of the Serenissima, and erect statues to Morosini and Dandolo. I'll give one up on you: the titles of duke of Venice and duke of Dalmatia might be added to the royal titles, and the Sposalizio del Mare would be resurrected.