There is a BIG difference between God ALLOWING something to take place, and DOING something. Are you saying that God CAUSED Judas to betray Jesus? This would make Him the AUTHOR of Judas' actions. Because God KNOWS all things, does NOT mean that He CAUSES all things. There are things that God DOES, and others that He PERMITS. God in His foreknowledge SAW the evil actions of Herod, Pilate, Judas, etc, against Jesus, and USED these for the purpose of His WILL. Otherwise there is the problem that God actually MAKING these do evil against Jesus, and then also punish them for doing something that He instigated?
A good example can be found in the account of king Ahab:
"Then Micaiah said, “Therefore hear the word of the Lord: I saw the Lord sitting on His throne, and all the host of heaven standing by, on His right hand and on His left. And the Lord said, ‘Who will persuade Ahab to go up, that he may fall at Ramoth Gilead?’ So one spoke in this manner, and another spoke in that manner. Then a spirit came forward and stood before the Lord, and said, ‘I will persuade him.’ The Lord said to him, ‘In what way?’ So he said, ‘I will go out and be a lying spirit in the mouth of all his prophets.’ And the Lord said, ‘You shall persuade him, and also prevail. Go out and do so.’ Therefore look! The Lord has put a lying spirit in the mouth of all these prophets of yours, and the Lord has declared disaster against you.” (1 Kings 22:19-23)
Here we read of a spirit that came before the Lord as said that he would be a lying spirit in the mouths of these prophets, who would give false instructions "in the Lord's Name" to go to war and die, so that the purposes of God might be accomplished. Because the Lord ALLOWED this to take place, He did not DO it Himself, as the spirit did it, it could be said, "The Lord has put a lying spirit in the mouth of all these prophets of yours". It is IMPOSSIBLE for God to CAUSE any person to lie, and therefore sin, but PERMIT this to take place as He does use evil deeds to accomplish His ultimate purposes.
I am still looking for the word "allow" in Ac. 4. 27, 28. I think your issue seems to be a lack of understanding of the nature of second causes. The following is taken from the 1689 London Baptist Confession of Faith and sets forth what I believe the scriptures to teach on this issue:
God hath decreed in himself, from all eternity, by the most wise and holy counsel of his own will, freely and unchangeably, all things, whatsoever comes to pass; yet so as thereby is God neither the author of sin nor hath fellowship with any therein; nor is violence offered to the will of the creature, nor yet is the liberty or contingency of second causes taken away, but rather established; in which appears his wisdom in disposing all things, and power and faithfulness in accomplishing his decree. Although God knoweth whatsoever may or can come to pass, upon all supposed conditions, yet hath he not decreed anything, because he foresaw it as future, or as that which would come to pass upon such conditions.
O the depth of the riches both of the wisdom and knowledge of God! how unsearchable are his judgments, and his ways past finding out! -Ro. 11.33