Thank you for your question
My name is ***** ***** I shall do my best to help you
I am afraid that the Judgement can indeed be Registered in the UK and enforced here, and your new home could be at risk.
However whether you hold as Tenants in Common or as Beneficial Joint tenants ONLY your share of the matrimonial home is at risk - if a Charging Order is issued it immediately severs the Joint Tenancy.
I hope that this is of assistance - please ask if you need further details
Only your half share of any equity is at risk.
Have you looked at enforcing the order in Ireland and forcing your ex to pay?