As with many American visitors to Ireland you may well be planning to cram too much into too short an itinerary.
If you only have 3-4 days I would plan a single location within an easy drive of Dublin and use that as a base to explore and return to every night rather than pack,drive,see,unpack and repeat particularly if it's wet and windy.
If you have kids I'd also choose a holiday rental over an hotel - I'm not sure how old your children are but Ireland in winter is a tough call to keep them happy and a nice cottage with a real fire and a trip to the local pub might be more family orientated than a hotel.Ireland,by the way,is very relaxed with children in pubs till a reasonable hour (9pm).
I'd recommend Homeaway and Tripadvisor for holiday rentals.
As for location I would choose somewhere not too remote - Cork or Galway are good options with excellent road links.
As others have said Ireland is a modern country that functions just like any other in winter time but it is still a piece of rock in the Atlantic that can but not always get stormy.
A great country to visit though.