Legally, no, absolutely not. A legalized death penalty causes all sorts of problems.

However, I don't think I would have many reasons to hold back if anybody were to harm the people dear to me.
The only reason for me not to torture and kill somebody who would've killed someone close to me (maliciously and on purpose), would be the fact that me going to jail would hurt the remaining people close to me.

If none were left however, I would most likely go all out and make sure that nobody could stop me from unleashing hell on earth for the responsible people.

Would happily accept any sort of divine retribution with open arms as well at that point.

Alas, I still disagree with the death sentence, mostly because corrupt assholes would use and abuse it for various nonsensical reasons.