How we feel morally about the death penalty is often just a result of chemicals in the brain. Most men feel a flush of pleasure whenever someone they think deserves it is hurt in some way. Most women, on the other hand, while not empathizing very strongly, or at all, don't usually feel pleasure. I'm not like most men, I never really experienced anything from having someone I hated hurt. That doesn't make me morally superior, I wouldn't pretend it does. It's just how I am.
However we must realize that if you only believe in the death penalty because it makes you feel good, you are essentially just being selfish. It costs a lot to ensure a fair level of due process that we expect in a modern society. Even the cheapest system would execute a lot of innocent people and wouldn't be much cheaper, or cheaper at all, than simple life imprisonment.
Of the other hand, the family members may experience pleasure from having the convicted put to death, which would could technically make it worthwhile. Then again, I don't really think a small feeling of pleasure would make any lasting, real contribution to their emotional state. Much better it is to just put them in prison and be done with the whole affair.