I don’t really see how they got duped by the committee, they thought Dani wanted Tyler gone, were they trying to do the opposite of what Cody wanted?
You said it. They THOUGHT Dani wanted Tyler gone. That's how they got duped. They THOUGHT Nicole was going to vote out Tyler and that Dani would break the tie to keep Ian. They got duped because The Committee knew the plan.
When the Power of Love overcomes the Love of Power, the World will know Peace