The concept of hell in Islam is covered here:
philosophy-dubai/life-after-death-according-islam-t11871.html#p109703The reward and punishment in Islam on the day of Judgement is in the hands of God - and He decides. There is no teaching, to my knowledge, that a criminal who is punished on earth is absolved from punishment after death. The criteria is rather whether the person has reformed/repented and whether God forgives him or not. And God only knows what will be the judgements after death.
For the family to not wish the killer of their child to live and to wish him to rot in hell (as it were) - is a totally understandable human emotion. The state should take into account the feelings of the family when deciding on a just sentence. The circumstances of the offender, the mental state and any other relevant facts should be taken into account. In this case, I can't see why the state shouldn't impose the ultimate penalty - and it is the family's right to forgive or not forgive.
I would expect the man to suffer after death the punishment of God too - but only God knows whether he will or not.
(I've not chosen to comment - as I've already posted many times where I stand on capital punishment - that I'm in favour of it as an ultimate punishment in a justice system with adequate checks and balances. In this case I hope the killer's death gives some closure to the family.)
Cheers,
Shafique