We went to Ireland and England in 2023 and had 10 days in each place, which for us worked out well.
I just have never seen the appeal of Paris, so we made no effort to add that on. For me, at 11 nights abroad you are already on a tight schedule. Rather than cut Ireland, I would cut Paris.
We only spent a couple nights in Dublin with one being the night after arriving. I would recommend doing that just to get yourself acclimated and sorted. We then went over to Galway for a couple days, then spent the night in a castle in Clifden, then down the coast seeing the Cliffs of Moe, few nights in Killarney, a night in Kilkenny before heading to England. Based on your overall schedule, I would spend a night in Dublin then head to Killarney for a couple of days.
Keep in mind that you should not have to clear immigration again between Ireland and England, sop we just took a RyanAir flight.
So much to see in London and the surrounding countryside. Prioritize what your family is most interested in. We spring for a private guide in London that packed a ton into one day. Highly recommend. We also had a guide take us through the British Museum. He is an Egyptian archaeologist and he brought the museum alive - even quizzed our 13yo on what he learned with right answers allowing steps to exit and wrong answers meant taking steps back. Priceless experience.
We also had a guy take us on a day trip out to Avebury to see the stones, Glastonbury to visit King Arthur's (supposed) grave, and Stonehenge. That was pricey but for us it was again worth it.
Enjoy the trip. You cannot go wrong if you focus on what interests you the most and remember to have a little downtime on vacation even if it's an afternoon at a pub to plan the next day.