A brief illustration of human nature -
"All I ever did was try and help people to have a good time ..."
that quote is by Al Capone, one the most notrious, not to say vicious and vindictive criminals in American history.
It illustrates that human nature makes it hard for people to accept that they are inherently evil, and have done terrible things for which they must be punished.
That explains the raison d'etre of the appeal.
But in the world of law, where human nature plays no part, sentences are debated and set by legal minds, without the input of any emotion or revenge - and that is as it should be.
So although Mairead Philpott is entitled legally, if not morally, to appeal her sentence, I would suggest that it is unlikely to be considered for reduction, given the circumstances of the crime for which she was imprisoned.
To address your specific question baz - it is likely that Mairead Philpott does not think she deserves to be in prison at all - but again, her input is not required or included in the judicial system.