... but one has to think of the greater good ...
That's why Harry was still alive.
But still, Titania experiences the agony of loss, and rage against the instrument of her loss.
... Aurora's death was painful and slower, that's what Titania cannot forgive ...
It was painful, yes. But still only a matter of a few minutes, at most. Not lingering in extended agony (as some mortals must (as Aurora's co-conspirator Lloyd Slate did)).
... I don't know what you mean about Mab "getting it out of her system" before she realized that Maeve was infected beyond help and had to die.
Not
before she realized, but
when she realized. We don't know exactly what happened. But several books before Harry is ordered to kill Maeve, Mab showed up using Grimalkin as a her sockpuppet. I understood that to be Mab's 1st scene after learning that Nemesis had taken Maeve (and thus, that Mab herself would most likely need to arrange Maeve's death).
By the time of Cold Days, Mab has somehow "gotten it out of her system" (or "come to terms" with it, however you want to say it) and she is able to speak normally.