Finally, Ireland has the ability to veto any deal the UK attempts to make with the EU

nope, Article 50 is under QMV:

That agreement shall be negotiated in accordance with Article 218(3) of the Treaty on the Functioning of the European Union. It shall be concluded on behalf of the Union by the Council, acting by a qualified majority, after obtaining the consent of the European Parliament.

as are any trade deals (mixed agreements come in two parts, 99% under QMV, <1% under unanimity, can come into effect without the 1% as CETA has, even though it has not been ratified): Article 207 TFEU

1. Where agreements with one or more third countries or international organisations need to be negotiated and concluded, Article 218 shall apply, subject to the special provisions of this Article.

The Commission shall make recommendations to the Council, which shall authorise it to open the necessary negotiations. The Council and the Commission shall be responsible for ensuring that the agreements negotiated are compatible with internal Union policies and rules.

The Commission shall conduct these negotiations in consultation with a special committee appointed by the Council to assist the Commission in this task and within the framework of such directives as the Council may issue to it. The Commission shall report regularly to the special committee and to the European Parliament on the progress of negotiations.

1. For the negotiation and conclusion of the agreements referred to in paragraph 3, the Council shall act by a qualified majority.

No veto