Under what circumstances would the conflict between the Austrian Empire and the Kingdom of Sardinia disappear?
It depends on the specific situation. In any case, Palmerston wouldn't naively believe that Austria, after rallying its forces to march into the Kingdom of Sardinia, would easily let Sardinia off the hook for the so-called world peace.
Thus, it comes down to one party falling. It takes two to tango, and the conflict naturally ceases to exist once the enemy falls.
Without a doubt, the one falling now must be the Kingdom of Sardinia. Palmerston surely doesn't believe the People of Sardinian could turn the tables.
Even if the remaining Sardinian Soldiers were to transform into Spartans, it wouldn't change the outcome of a lost war.
After some thought, Palmerston said, "Mr. Metternich, for the sake of world peace and stability, the British Government suggests that your country promptly end the Ausa war and revert to the status quo ante bellum."