“Can you tell me what Article and Section gives this power exclusively to the Executive? I’ve been trying to find it.”
Article II Section 2. The senate is required to approve treaties, the President alone can negotiate them. Diplomatic appointments, again, must be approved by the Senate, but the power to appoint is exclusive to the executive.
As for the power to remove ambassadors, or dismiss ambassadors from other countries, the Constitution is not explicit on the matter, but the writings of the founders, and subsequent case law, make it clear that this power belongs to the President alone. It is implicit in his exclusive power to appoint ambassadors that he is the only party who can decide what nations to recognize and establish relations with.
So with respect to Israel, the negotiations that the Administration conducted regarding the UN resolution should have consulted the Senate and received 2/3 approval before it went to the Security Council?