London to Ireland, is this doable?

Hello all!
We are trying to plan an add in Ireland trip with our visit to London. We have never been to Ireland, but would love to see a few sights. We aren't trying to overextend ourselves, as we would be traveling with a four year old and 14 year old. So if this tentative itinerary isn't doable, please advise me! We are making the annual trip to London( into LHR) to visit my father. We would stay there 5 nights. I have taken both children alone several times, but husband is joining and would like to see some of the major sights in London this time. I hoped that we could hop on a cheap flight from LHR to Shannon ( I heard customs is easier at SNN than DUB.) We would rent a car and would like to see the Cliffs of Moher and Cashel ( stay near there for 4 or 5 nights?) . Then we would drive over to Dublin and see a few sights there( staying maybe another 4 nights before taking a flight from Dublin back to LHR. From there return on our flight to the states. My main question is, how many nights on each side of Ireland, what are the top 3 sights we should see on each side of Ireland and is this doable with a 4 year old for that timeframe? Thank you so much!