Bechirah, free will, only works in cases where Yiras Shamayim[fear of heaven] can be involved. If you think about it, though, even the most mundane situations can involve a Mitzvah or Aveira. An example given on the forum was painting a room. It may not seem to fall under this category, but if you wanted to, you could decide to pick a color people would like and would make the room seem more cheery, or you could pick a color you like, but makes most people feel nauseous. That is a Yiras Shamayim case, and you would have free will.
The rule is this: If this decision would be made differently by Moshe Rabbeinu than by a Rasha, it is a Yiras Shamayim decision and Bechirah plays a role. If Moshe Rabbeinu and the Rasha have no reason to make different decisions then it is a non-Bechirah decision.
When you rebel against Hashem, Hashem allows you to make the decision to rebel, and then, yes, He actually causes you to bring the decision to sin to fruition. Although the decision you made was against what G-d wanted you to do, but it is not dualism because it is the Will Of G-d that you should be able to go contrary to His preferences if you so desire.
It's like when you allow your kid to do something you don’t want him to do, knowing he will get hurt doing it because that way he will learn "the hard way" and be able to ultimately function better on his own.
So too Hashem allows us to do wrong because without the ability to choose wrong, we would never develop the ability to choose right over wrong.
