Knowing what I know of folks in the Republic of Ireland, I'd say the chances of the Republic joining the Commonwealth approaches zero. Too much has been gained there by EU membership, Euro use, and free travel to and from the continent.

The thorn in the border with Northern Ireland, as the law grants citizenship to individuals born in Northern Ireland under the same conditions as those born in the Republic of Ireland. In short, those in NI can also claim citizenship in the Republic if they wish and I suspect that many would do so (not the DUPs, of course).