Is it too much to do Dublin, London, and Paris in two weeks?

It can be done. You probably won't see everything you want to see. You will spend time traveling between the cities. Depending on the time of year you go, the crowds may make it difficult to pack things in. (If you can avoid travel in the summer it will be easier.)

But three cities in two weeks is not impossible. I wouldn't add a fourth but perhaps a day trip outside of each one.

My only suggestions is to minimize your travel time once in Europe. Some will tell you to take a ferry and a train from Dublin to London. That will take up an entire day. Fly. It's quicker. Between London and Paris stick to the Eurostar. It's faster than flyiing when going city center to city center.

Much easier done if you fly Dublin to compact London City Airport. (LCY) and take the Eurostar from London to Paris..

How many nights will you sleep in Europe? Have you checked air prices flying multi-city? An example is flying into Paris and out of Dublin, etc. If you fly round-trip in and out of Dublin fly to Paris on arrival day and save Dublin for the end of your stay.
Don’t expect to do much sight-seeing on arrival day. Instead, settle in then stay on your feet. Visit museums the next day.
I feel Paris deserves five night, London six nights and Dublin three. If you add day trips add a night per trip.

Use Kayak.com to check and compare flights.

My advice is always to get over the Atlantic Ocean on the best flight for you, whatever that means. I just got back from a two-week (left on Saturday, got home on Saturday, so 12 days on the ground) trip SEA-FRA round trip, train to Amsterdam, Eurostar to London, fly to Cork, train to Dublin, fly back to FRA. The purpose of the trip was a job fair in London. We chose the Frankfurt flight because I could get premium economy at a good price. We lost a lot of time traveling between cities. We chose Amsterdam because it’s on Eurostar and is not Paris (too big for our timeline). I am an experienced traveler. All this is to say that just because you fly into Dublin doesn’t mean you have to visit Ireland. Fly right out again (leaving time for delays, of course). Use Eurostar between London and Paris. You might have to stay the last night at Dublin airport, but lots of people do that on their Ireland trips, too. But check with the family. Maybe they will want to see beautiful Ireland instead.

I don't know when or if we will be back.

Don't sell experience short, spend a little more money.

Assuming 2 days for travel to and from US (unless you planned trip to encompass 3 weekends), you have 12 days on the ground, so 4 days per city. I think that's dooable and I don't think you should fly into Dublin without allowing a little time for Ireland. I suggest you take a day tour from Dublin to Glendalough. Since you should be in Dublin the day before your flight to the US, you should do Dublin last. How are you planning to travel between cities? People say that there are cheap flights between European cities, although I have never done that.

"People say that there are cheap flights between European cities"
There are. I use skyscanner.com to find them. You just have to be very careful about the baggage limits, both dimensions and weight, for personal items, carry-on AND checked bags.

We definitely plan to explore Dublin. Just wasn't sure if we could fit in one, two, or no more cities in that timeframe.