GLADSTONE - I have the greatest admiration for any C19th English PM who could say, "My mission is to pacify Ireland", without pacify being a euphemism to exterminate or mulct Catholic landowners. (My real name is Patrick Francis Domenico Xavio Leonard - I reserve the right to opine on this matter).
I have a particular disdain for the crackpots and cynics of Saxe-Coburg-Gotha. Therefore Gladstone scores again if Queen Vicki's having the, "... greatest possible disinclination to take this half-crazy and in many ways ridiculous old man." (on his third go as PM) is correct. (Parliament had a problem with her having wanted to make her hubbie Prince Albert of, you guessed it, Saxe etc. co-monarch and heaped many indignities upon her 1st Cousin/Husband.)
Why not Disraeli? Too occupied with English affairs for a later C19th PM and didn't give a fiddler's fart for Ireland which he indirectly re-beggared with his refusal to protect British and Irish agriculture in order to provide the cheap, imported food to feed the great British Unwashed.
Hail Caesar! This diverts my ageing attention from Everybody Loves Raymond re-runs but mid-C19th British Parliamentary politics are mind boggling and your questions is vexed. The Party system existed but was flexible. At one point Disraeli was eager to co-opt Gladstone's services in the post-Palmerston years.