To me you can feel hatred to the depths of your bones for someone who has committed a horrendous crime against a loved one and wish them great sufferance and die. But still I would say, No, to the death penalty. It is not the answer.
To my way of thinking, if you say yes to the death penalty then you too become a murderer. I would think having a chance to tell the perpetrator face to face what you think and feel would be a good start to your revenge and healing. And then? You can only hope that either what was held dear and close to the perpetrator is taken away from them during their prison time. Or, they have to in some way pay back by having a role in relieving the suffering of another person while in prison or out in the community till they die of natural causes.