I think a better question than “Why would the vice president stay at Trump International Golf Links in Doonbeg when his meeting was in Dublin?” or “Why would he pay for this visit out of pocket?” is “Why would anyone, at any time, stay anywhere that was not Doonbeg?”
Consider the facts. Doonbeg is a paradise on Earth. It has everything that an International Golf Links ought to have: the Trump name on it, in big letters, and also, I am sure, many other benefits invisible to the untrained eye.
Besides, Dublin is a wretched spot.