I rather read Judas' betrayal as a display of God's omniscience, not his pre-determination of our sins. God knew that Judas was going to sin, perhaps He sees all the myriad possibilities, I don't know, He is GOD.
I have nothing but utter and complete sympathy for your position on this because it was mine until just recently. :) I believe that you can know for sure that God sees all the possibilities. I believe that God knew that Judas was going to sin from before the earth was formed. He also knew exactly how it was going to happen, and for exactly what price.
If God is perfect, and if God already knows these (above) things, and if God could not leave anything to chance (i.e. outside His knowledge), ... then did God allow or "cause" it? Yes.