I'm so sorry for the callous and vile way your cousin treated you when being vulnerable about what happened to you. No family member should be so heartless. No mental health worker should be so heartless. No human should be so heartless. Yet it just goes on and on, and families, mental health "professionals" and supposed humans continue to perpetuate wrong unto those who have already been so innately wronged. I'm sorry.
I don't know how I feel about any death penalty for any crime. I don't really know how I feel about most things, admittedly, but I particularly ruminate often enough on how I personally would "fix" the justice system. I never come to any actual conclusion. One day I might agree, "Off with their heads!", another day I might think that the ongoing punishment of life imprisonment is more fitting. What I find hardest are the cycles that begin early, and then snowball. This is not related to sexual offences, which are particularly vile, but I do think a lot about teens who make a single poor judgement, maybe throwing stones at a passing car, say. Then the twisted justice system ends up pushing them deeper and deeper, and their offences grow and become worse, and one silly mistake that a teenager makes ends with a lifetime of waste. I wish we could fix that. Some people are probably what would be considered 'bad' to begin with, and that cycle can't be broken. But I do earnestly believe that some people just make an adolescent mistake that follows them forever.
Sexual offences, though, are one of the worst things people can do to other people, though. They are torturing another human, and that needs to be punished. I just don't know what I think is the most appropriate punishment. What @waqs had to say was very insightful, too. If whatever punishment is applied in some way harms the victim further, that's just cruelty beyond belief.