This was our third cruise, but the first in 10 years and the first with children (ages 7 & 5). We picked Carnival only because they are the only cruise line offering shorter cruises out of Galveston in the summer (we live in Houston). Also, we had heard good things about Carnival's kids club.
You would never know the trauma that the ship went through earlier. It looks & functions fine. The public areas are very nice. The formal dining rooms (Paris & London)are beautiful as is the main theater (the Rome lounge). So are the main lobby,the casino and the other lounges/bars inside.
Both embarking and disembarking went very smooth.
Our room was ample enough for the 4 of us in terms of storage space, bathroom space etc.The ocean-view window was large and I did not really miss the balcony we had on earlier cruises. We were on deck 2 which was very convenient to access the formal dining rooms and the Rome lounge on deck 3. The one complaint I have about the room is that the sofa does not fold out to make a bed for two. Rather it simply has a single mattress. To accommodate the 4th person Carnival had a small mattress/bed-spring that stores under the main bed and that they place on the floor next to the sofa sleeper & leave there. It was fine for sleeping but intruded on the floor space and left little room for walking from the door to the main bed.
Triumph has 3 pools. All are outside, shallow & salt water. None is big, even the center one on Lido deck where outdoor events occur. This pool becomes overcrowded & unusable at times. The pools overall were a disappointment.
Other outside stuff includes a nice water slide, a basketball goal, 9 hole mini golf (very popular), a ping pong table (broken) and a fenced in toddler area with slides etc. and a number of peddle cars/trikes (most broken).
Service in the dining rooms etc. was excellent.
A negative was the fact that many of the activities on the schedule were geared to getting more money from the passengers. "Free" seminars for example. Carnival sets up lots of opportunities for paid photos (getting on the ship, getting off the ship, dress elegant night, dress casual night etc.). My wife happened to ask our steward where he learned to make the towel animals and he instantly produced a book on this from his cart, for sale. And Carnival charges for drinks in the casino, unlike every land based casino I have been to. It was too much.
The shows in the main lounge (Rome) ranged from so so to excellent. A couple were quite elaborate. The lounge itself is very nice & large & never filled up. We did not catch any of the comedy or burlesque shows.
The food in the main dining rooms was very tasty, though portions were on the small side at times (hey, we're from Texas!). One could always order more. The your choice dining (versus set time) worked well for us & we only waited once for a table (for 30 min). The buffet restaurant on Lido deck was convenient and had ample seating but the selection was not as varied as I would have expected on a large cruise ship and the quality was so so. We tried a couple of the specialty food outlets (Guy's Burgers and Pirate Pizza) and they were fine though not exceptional.
We put our kids in the kids club 2-3 times for 2-3 hrs each time. Our 7 yo son always enjoyed it. Our 5 yo had mixed reaction due to the fact she was with a 2 - 5 yo group that she felt was babyish at times. It was generally convenient but they do close for 1 hr for lunch & 2 hrs for dinner so you can't leave your kids there literally all day.
Carnival has (or had) a reputation for being more of a party cruise line. We saw this to some extent (compared to our previous Princess & RC cruises). This cruise probably would not be the best choice for older couples or families with small kids (like us). Overall it was not bad, but frankly, we did not have the same sad feelings upon disembarking from this cruise as we had on our other cruises.
We did not book an excursion in Cozumel. We got off the boat and caught a taxi ($11) to Chankanaab park. Cost for the 4 of us was $70 to enter the park. This is a nice place. Be aware that there is not much actual beach. The only beach is along a small natural pool that connects to the sea by some small passages through the rocky coastline. This pool is about 3 - 4 ft deep, and had a lot of fish in it. We found a very nice flounder hiding in it. It is a great place for smaller kids to swim and snorkle. A caveat is to do this early as once more people show up the pool gets cloudy from people (sandy bottom) and one can't see anything. The sandy beach by this pool, while not large, was enough for us. If you want a large beach along the sea there are better choices in Cozumel (but w/o good snorkeling).
Along the rocky coastline there are several places with stairs to make it easier to enter the water. Around these it is fairly shallow and a good place for kids/weaker swimmers to see fish. Moving away from these stairs and going along the shore there are lots of fish. There's not a lot of living coral but there is some. Lots of sea fans. It does get deep quickly as one moves away from the shore. There is a floating platform anchored out there near some nice coral heads. I've snorkeled better places but this still rates well.
The standard dolphin encounters are quite $$$ (packages at $190, $150 and $100 pp is what we were first offered) but after we balked at the $$ the staff reluctantly pulled out an offering (not associated with Carnival) for a picture & limited dolphin interaction for a total of $70 for both kids. This ended up being a great deal. It lasted about 15 min total and my 2 kids had a dolphin to themselves. There was plenty of interaction, including a dorsal ride (with 2 dolphins) for my 7 yo son. The included pictures (one of each kid) came out great. We also saw the included (free) sea lion show at the park.
Chankanaab also has a swimming pool that is much nicer than the pools on Carnival Triumph. We only had 6.5 hrs ashore in Cozumel so we couldn't enjoy Chankanaab as much as we would have liked. It does make for a great day ashore.
In Progreso we caught a cab to Merida so didn't see a lot of the town. We did get a look at the beach & water there along the shore in Progreso. It isn't great. Better than, say, Galveston, but not nearly as good as Destin or Cozumel.