the italian policy MUST give minimium Irish cover whilst the car is being used in Ireland. That means that the italian company will pay you, assuming that the italian driver is in the wrong. from what you say, that should not be a problem. If he pleads guilty to the driving charge or to a lesser charge, then that goes against him in the Civil claim, but if he pleads not guilty yet is found guilty by judge, that does not go against him in the Civil claim.
You should immediately contact the MIBI who will make contact with the italian company and arrange for the italian company to appoint an irish handling agent, that is an irish company, so that you do not have to go to the trouble of phoning/writing to italy, but can contact your local company.
Another option, is for you to claim under your own policy if comprehensive and let your company follow the matter up with the italians.