3 Days in Dublin with 10 and 13 yo?

I think the 10-year-old might be a bit young for the Kilmainham Gaol. Also, Trinity College doesn't have much to offer this age group. EPIC, on the other hand, is accessible to a younger audience. I haven't been on the Jeanie Johnston, but I imagine that would appeal. Dublinia, which I also haven't been to. The "dead zoo" aka the Natural History Museum. And the Archeology museum has bog bodies. The 13-year-old might enjoy reading Bog Child by Siobhan Dowd in advance of your trip. It's a YA novel partly about The Troubles. Very engaging. And it involves the discovery of a bog body. I hope you're taking them to Newgrange. A day trip to Howth for some hiking and cliff views? Not sure whether this is a layover or part of a larger trip to Ireland. I really like the tea bus, https://www.vintageteatrips.ie
But there is a Viking Splash tour that might be of interest. https://vikingsplashdublin.ie

Maybe a tad morbid, but as a science nerd, I loved the big bodies at the Dublin museum of natural history, which is possibly closed for refurbishment but the website is confusing as all get-out!

National Museum of Ireland. The website has bog body info. I suggest visiting museums' sites to see what exhibits and special exhibitions they have. Sometimes museums have projects/info for kids

Your family is going to love Dublin. I just returned with my family, all adults. I can give you some insights that may help you make a decision for your children.

• Trinity College Book of Kells Experience might be the right choice for you. There are other tours like the one we took with a student guide around the college that is better suited for older teens and college-aged adults. The Book of Kells itself and the old library is a self-guided tour and the Book of Kells is such an important document and so beautifully illustrated that your family may enjoy seeing. The library itself is under renovation, but still has some books in the stack and is an example of a glorious old library. The Book of Kells Experience in the Red Building is interactive with a fun multimedia show. Depending upon the time of day you go, there is a nice little cafe for the students or alternatively you can get a coffee or pastry at the coffee carts before your visit. If it is a nice day, you can picnic on the grass along with the students.
• Kilmainham Goal is a 45 minute tour through the most important jail in Ireland. The tour itself is interesting as it talks about how the jail was envisioned and then how during the famine, it was used to house people (including a child as young a 3 just for stealing food during the famine), the tour spends time on the history around the Easter 1916 rebellion and you get to visit the cells and tour the yard and the main holding area (which is seen in so many films). There is an excellent museum that you can skip if the tour was too much. Before you book, I would go online and have your kids look at the jail and see if they are interested. If they are, then plan purchasing your tickets right when they go on sale. Some joke that it was easier to get Taylor Swift tickets than tickets to Kilmainham. I had to switch days as I wasn't fast enough to get my order in the first time I tried. The museum has an okay coffee shop, but no air conditioning, so I would not recommend that you eat there if it is hot.
• EPIC museum & Jeanie Johnston: both of these would be appropriate and fun for a 10-13 year old. EPIC tracks the emigration and impact of the Irish across the global. It has fun and interactive activities. You get a passport that you stamp along the way and can take home as a souvenir. If your kids are into sports, that area has a place to create your own logo & dress up. Jeanie Johnston is an intimate experience on a famine ship. You can book tickets together to save money. Also go to EPIC early. The website says they open at 10, but they don't they open at 9:00. You can each at some excellent options in the complex as well. If you are doing any genealogical research, you can also book time at EPIC with a genealogist.
• Pubs: my group was not a fan of the Temple Bar area. Much of the music there is not traditional music and it was a bit sketchy. You are from NY City, so you can deal with the people who come up and ask for money and hassle you. I am from SF and it was fine, but my family from Arkansas was not comfortable and we weren't even out late (around 9:00 p.m.). We visited some pubs outside the Temple Bar are, two to try are the Brazen Head and the Gravediggers. We especially loved the Gravediggers. It is alongside a cemetery and has great food (just don't go on Monday). People there are super friendly and we spent hours in the pub just chatting. They recommended Cobblestone for trad music, unfortunately we didn't make it.
• Pubs/Show: Johnnie Fox Pub is the highest elevation and offers an excellent Hooley show that includes phenomenal food, trad music, and dance. You can reserve a shuttle from Dublin.
• Dining: If you are in Dublin on a Sunday, then the Old Spot has an excellent Sunday roast. You can also try to combine your visit to Brazen Head for their Sunday roast.

I agree the Brazen Head was excellent. In this and most all pubs, there is SO much to see inside. And the pubs are not just a bunch of young folks drinking, there are many families and young children in them having a meal.

As for the Temple Bar (the bar itself), we had a great time listening to some very good trad music, but even at 2 pm on a weekday, it was jam packed with people, and might be pretty hard to find room for 4. I think the kids need to hear some real Irish trad music, see how they like it.

This link is a great source for Trad Music in Dublin: The Session