Could you get an up-to-date valuation on the Kildare property done without spooking the tenant? That will give you a clearer picture of where you stand with negative equity.
Ask yourself if being a landlord with an investment property is something you want to be in the long-term or has it just been an evil necessity?
Then if it's just been a necessity ask yourself how you will best extricate yourself from that situation.
You could do as has been suggested - sell & take the negative equity with you to a new property in Dublin. If you buy the right property in Dublin that negative equity may be reduced much more quickly than it will be in Kildare by rises in property value.
You could wait for a year, save as much money as you can over the year & see where you are then with regards to the amount of negative equity on the Kildare property. You'd have saved money to pay down that mortgage or as a deposit in Dublin.
Unless you really want to have an investment property, make your life as simple as possible & have one mortgage on the property you really want to live in. If that's your decision, then the only other question is one of timing - when do you sell the Kildare property & that becomes an issue of property price speculation & how quickly you want the simpler life.