Help with General Plan

If possible, hold off purchasing airfare until you have firmed up the itinerary. An open-jaw flight plan could save you a lot of backtracking time at the end, plus it would allow your itinerary to flow in a logical and efficient manner.

Well, the flight is locked in unfortunately, it was booked a looong time ago.

Maybe extend your time by 1 extra night in some of your cities (i.e., Paris or Rome).

Another alternative since you have to go back to Ireland anyways, find a cheap flight from Italy to either Northern Ireland or Western Ireland. Belfast and Galway both have easy train or bus connections to Dublin for your return flight home, and both make good bases to explore surrounding countryside, or stay put and enjoy Belfast or Galway.

All advice I have ever seen is that Normandy is not really doable as a day trip from Paris. If I understand your schedule correctly you only have 3 full days scheduled for Paris. Have you been to Paris before? Considering the time of year you will be there and dealing with lines at attractions, you are not allowing enough time there IMO, especially if it is your first time. How are you planning to get from one point to the next? You need to allow time for transportation and Paris is quite a distance from Rome unless you plan to fly.

I would skip Italy and spend more time in Germany and/or Belgium (personally I'm not a fan of Amsterdam, though many enjoy it) and more time in Paris. Then you could do 1 - 2 nights in Normandy. If you don't venture so far away you won't spend so much time traveling and you will have more time to enjoy where you are.

If you are going to the Normandy region, I'd skip it if you are doing it as a day trip. An overnight trip is really better because the area is spread out, and there's a lot of time to be spent there in order to apprecate it. Do not go just because its there.

We rented a car and drove from Paris to the D-day beaches, and drove to the Mont St. Michel abby, spend the night at a chateau near MSM and then drove back to Paris, with a stop at Bayeaux. It was the best "side" trip ever!

That's probably what I'm going to do then, just forget trying to add one more city and just do more in the cities I already have. I'm not relegated to just a day trip in Normandy, it is quite possible to extend that to a full day or two. But, I assume that is more than enough time for a Versailles trip?

If you are at Versailles when they open you can probably manage it in half a day.