No, I would not have a different outlook were my child to die of a heroin overdose, because were that to happen, it would be because my child chose to take heroin. That's a stupid thing, and a death from it would be tragic.
However, that does not change the reality, as I see it, that the death penalty is a disproportionate punishment for anything other than pre-meditated murder, and that even in that case, in the modern world it is not truly necessary.
Putting people to death for murder, even, in the modern world is at the limits of propriety. Putting anybody to death for anything short of that is barbarism, plain and simple.
General Washington hanged men for mutiny and for espionage. Was he therefore "barbaric"?
And what about those who profit wholesale from dangling the poison of life-destroying addictive drugs in front of confused and impressionable young people? I suppose you wouldn't consider that barbaric.
When Julius and Ethel R. handed off our nuclear secrets to the soviets, they handed them the means to murder every last one of us. That may not be "barbaric" enough for you, but in my view, it qualified them both for the death penalty.