> As for the victim's family "control", are they really in control? Where they the ones condemning the victim?
Sharia law distinguishes three types of crime – hudud, qisas, and tazir. A hudud crime is one where the penalty (whether death or some lesser punishment) is mandatory under the law, and so must be carried out (although there are various mitigating principles which can be used to justify not doing so in a particular case). A tazir crime is where the penalty is up to the discretion of the judge (and the ruler of the state as lawmaker). A qisas crime is one where the punishment is "eye for an eye" retribution, and hence the victim (or their family) has the legal right to commute the punishment. Murder (in most cases) is a qisas crime, so the family of the victim has the legal right to commute the death sentence to a lesser punishment, and no execution will be carried out without the consent of the family. This is different from hudud or tazir crimes, where the victim (if there is one) has no legal entitlement to a say in the punishment.
An exception is something like a murder committed as part of a terrorist attack, which is simultaneously a crime against the victim (murder), but also a crime against the state (terrorism). Although the family of the victim still has the right to waive the death penalty for the qisas crime of murder, the state has the right to carry out the death penalty for the (tazir or hudud) crime against the state, so the offender will be executed irrespective of the family's wishes.
Honestly, although I am personally opposed to the death penalty, I actually think in some ways the Saudi system is less wrong than the US system. Under the Saudi system, an ordinary murderer cannot be executed if the family unanimously opposes their execution (in cases of disagreement, I believe Saudi law follows the wishes of the identified senior next of kin); in the US system, the prosecutors/courts/government are under no legal obligation to respect the wishes of the victim's family, and a murderer can still be sentenced to death and executed even if the victim's family are unanimously opposed to that outcome.
Also, although people denounce Saudi public executions as barbaric, I don't think private executions are any less barbaric than public ones. If anything, I think private executions are more barbaric, in that hiding what you are doing is a sign of a guilty conscience which knows it is really wrong. If voters can't stomach watching executions, they shouldn't be allowed to vote for them. (Saudis don't get to vote, at least not in any way that really counts–but it seems on this particular issue the Saudi government are doing the popular will–if you gave the Saudi people a free democratic vote on whether to retain the death penalty, I'm certain retention would win.)