To be clear, I do not support the death sentence in any circumstances. However, for anything short of a murder, capital punishment is actually an incentive to murder. Yes, these children will need a lot of help and many years to recover, if they do fully recover. But they are alive. And were therefore able to tell an adult what was happening and to testify. If victims aren't alive, then they can't report or identify their attackers. All the evidence historically and currebtly, suggests that the death sentence does not act as a deterrent for any crime, but that if the sentence for a lesser crime (such as rape) is death, then perpetrators may as well kill their victims as there is a chance that they will get away with it, and there is no further penalty that can be imposed anyway.
What you want is not justice, it is state sanctioned revenge. I have never seen the point in telling such people that they can have it if they are prepared to carry it out - the fact is that this is mob rule and of course they are willing to carry it out if there are enough other people with them so they don't take sole responsibility. Vigilantes can always justify their behaviour.
And if you think that jail is easy for child abusers, you clearly don't know much about jails. Even amongst criminals, there are hierarchies.