My husband and I recently returned from taking our 18-month-old daughter on her second Celebrity cruise. There are many reviews on this board attesting to the beauty and five-star class of the Equinox, which I would certainly second. The ship is top-class in its decoration and shows. I found some of the staff to be less friendly than on our first Celebrity cruise aboard the Summit, but that is personally relative. The dining room, though elegant, felt more squishy and our waiter had more tables, but I assume that that also varies from table assignment to table assignment.
From a mother's perspective, though, the Equinox was fantastic for those traveling with a young child. Since our daughter was under three and not potty-trained, she couldn't swim in the pool or join the Fun Factory activities. We knew that in advance and were just looking for a chance to hang out as a family without the distractions of everyday life. We were happily surprised to find the lovely, relaxed top-deck lawn that was perfect for little feet to release some energy. Also, between the stage and pool, there was a water feature (numerous small fountains at ground-level) that kept our daughter safely entertained. She never once looked jealously at the pool and she wasn't bothering anyone. Finally the Fun Factory had pretty loose "toddler time" hours so we were able to play with her using their well-kept toys and didn't need to devote much coveted luggage space to her toys.
Beyond those nice surprises, I'm happy to report the same joys that we had on the Summit such as watching her face light up with all of the great live music and being able to catch so much live entertainment (we always sat in the back so we could make a quick exit if needed).
Due to the fact that our server on the Equinox had five tables (15 people), it took a while to get the orders in (each course was served at the same time) and after the first four nights our daughter had had it with 1.5 hour meals. Instead we ordered from the Silhouettte dining room for room service a few nights and ate in the crepe restaurant or Oceanview Cafe the other nights. It was mildly disappointing not to eat in the main dining room but we also found the menu to be similar to our cruise on the Summit (on which we were able to eat every night with our then-9-month-old and a waiter that only had two tables).
At last, I wanted to say something about our fellow passengers and their response to our daughter. Conscious that most people aboard who were our age were probably parents trying to get a break from kids and no one, including us, can relax with a runaway or screaming child around, we always aimed to take our daughter out of the theater/dining area/public space if she started to behave badly. As I mentioned, we loved listening to the live music but we tried to keep to the side of the performers or to find an inconspicuous place for our tiny dancer.
Comparing the Summit (departing from San Juan on a Southern Caribbean cruise) and the Equinox, there were many more children on the Summit, which I attribute to the itinerary rather than the ship. The crowd on the Equinox was much more diverse- lots of French, German, South Americans and a ton of Russians and the crowd we overheard in the Fun Factory reflected that mix (mostly English as a Second Language learners). There were a total of six kids under three on the ship from what we saw on our 11 days on the Equinox.
All and all, I think cruising is a wonderful way to travel with a young child. This Ultimate Caribbean, with its historic/cultural interests as well as beaches, was a bit of a stretch for us but ended up being fantastic. If you're on the fence about cruising with a kid, I say go for it!
PS We had two cruise-sponsored tour excursions booked but ended up just doing one (Colonial Panama and Miraflores Locks- you can read my review in the Panama section). We pre-arranged Oscars tour in Puerto Limon and just caught taxis from the docks in Cozumel, Roatan, Cartagena and Cayman Islands. This gave us the flexibility to be where we needed to be at naptime and we could go at our pace. We travel a lot (60+ countries) and live abroad. We particularly had our guard up in Cartagena and it turned out to be our favorite port.