My flight lands in Dublin Airport at 1:10 am. By the time we are done with immigration and other checks, I am guessing it will be 2:00am. Are taxis available at that time? Also, we will be traveling with 2 kids and wondering if it is safe to take a transport vs. wait out in the airport for the morning.
Logic would dictate that if planes are arriving, there will be taxis available.
The issue to me seems to be where are you going? Does your hotel have a 24 hour reception desk? Have you made arrangements for a late ( early?) check in?
Dublin is only 15 or so minutes away , it would be very safe to take a taxi , and yes if a plane is arriving taxis will be there !!
As said though , check that you can check into your hotel at that hour !