You should try the Disney cruise. This is a top notch cruise line. They do have an adult only pool, restaurant and beach so you can have special time away from children while your own is enjoying the kids activities. The weather in January may be a bit nippy the first day down and last day back. At their private island you will probably have nice weather although it may not be hot beach weather and likely to be in the low 70s. But, the rest of your trip will be very warm. You can choose western or eastern caribbean. Both have their pros about them. On disney you will have a rotation of dining rooms different than on other cruise lines. Only one of the three is formal. The other two are casual, although they don't want you to wear shorts. You should eat in Animators Palate, Parrot Cay and Lumiere's and Lumiere's is described as "jacket recommended". But, having been on a lot of cruises I felt it more relaxed than other ships "formal" nights because not everyone is dressed up on the same night. I can't say enough good about the Disney product even for those without kids! It may not be the most relaxing trip you will ever take because there is so much you may find you want to do, but it surely can be. Be sure to book way ahead with Disney. With only two ships they book up rather early.

We just came back from a three day Disney Cruise this January and we loved it. To answer your questions. The weather in Florida and the Bahamas was in the 70's to 80's. The water at the beach in the Bahamas was a bit cool. The three and four day cruises go to the Bahamas and the private island. Since we had been to the Bahamas before, we took a quick taxi ride to Atlantis to see the aquarium and got back to the ship early. The day at the private island is easy. The ship pulls right up to it and you can walk off and just hang out at the beach all day long. You don't need to get all dressed up, just presentable. I wore a cocktail dress on the first evening and I felt overdressed. Nice slacks and a blouse are ok. You can also order room service or go to one of the other restaurants serving a buffet. There is a place by the pool where you can get pizza, chicken nuggets, tacos, etc. anytime during the day. But, I wouldn't miss Animator's Palate or any of the shows. Because it is Disney it is very child friendly, there are plenty of children at the restaurants and theaters. The shows are really good. The pools are very busy. They have a toddler pool that gets really full. The kids program is really nice and they also have a playground on Castaway Cay. They are extremely paranoid about germs the kids are "disinfected" with Purell before going into the kids club. I liked this. My kids always catch the germs. Also, they will not let anyone on the ship if they are sick with the flu.
The debarkation is the best I have ever done. I wish the other cruiselines would follow suit. You literally just walk off the ship when you are ready. There is no waiting for your color to be called. The customs agents process everyone very quickly.
If you go, don't miss the final night when the characters say goodbye, there is a special surprise for the kiddies at the end.
We booked a "guaranteed" inside cabin about 8 months prior and we got an early bird discount and were upgraded to an oceanview cabin. It was nice to have the window.