Concerning "double predestination"; I have had discussions with Calvinists that reject the doctrine of double predestination simply because they believe it makes God a monster.
They say that God predestines the elect, but not the non-elect. Yet, no matter how one tries to reason around it, if he predestines some to eternal life and leaves others in their trespasses and sins, He in essence is predestining both the elect and non-elect.
I tried to explain this to one and he insisted that leaving the no-elect in their trespasses and sins is not predestination.
So, at least in this case, I think it is the word predestination that is the problem, not the idea the doctrines is conveying.

Tom