Would you still feel the same if the person being put to death was responsible for torturing and murdering your loved ones?

No, since I am not mentally developed enough, I could not be rational but would instead be driven by feelings of hate and revenge, which is exactly the reason why verdicts in murder cases must not be based on the feelings of the relatives of the victim.

when I put myself in the victim’s shoes in certain cases, I completely understand the want for corporal punishment

Understanding such feelings is trivial. However, satisfying the victim’s family’s need for punishment on one hand and justice on the other hand are two very different things. The concept of “an eye for an eye” dates back to antiquity and has long been outdated.

It’s hard for me to say that the death penalty is absolutely never warranted, but I do think it should be very rare, and there should be an extra burden of proof to condemn someone.

I disagree. In any justice system, no matter how thorough, mistakes and false convictions happen. Also, societies always run the risk of slipping into authoritarianism and using the death penalty to eliminate opposition. See my comment above for more even reasons, they all apply.