Finding the correct Cruise line and trip for my 56-year-old mother

Personally I would look at itineraries more than demographics. With your mom's age, she will find plenty if folks on pretty much any cruise.

I would look at destinations and time in port. Some cruises spend much of the day sailing, others spend the day in port. The later offers far more opportunities to see and do things. Less time eating, more time exploring.

As commented by others it's not possible to point you to one specific cruise based on the criteria that you gave. I will however try to share some insights on the criteria I use when I have to decide on a cruise.

I cruised with Carnival, Princess, Holland America, Royal Caribbean and Celebrity so I can share some pro's/cons on these companies. Still, the staff, the ship, ports of call and your personal preferences can result in another experience than what I had.

Carnival: Call themselves the fun ships. This was one of my first cruises and I liked it then but after doing cruises with the other companies I really noticed a difference. The overall quality of food and service tends to be better on the other cruise lines. Carnival tends to be cheaper however. I appreciate good food and service so I never cruised with Carnival again afterwards but I think Carnival can be a good choice if you just cruise for enjoying the sun and the ports of call. That said, it wouldn't be my advice for a 56 year old, I would rather advice this to a younger public.

Royal Caribbean (RCCL): This was the second company I cruised with. They have changed a lot over the years and now make a point of having the biggest ships. "Our ships are huge" is one of their slogans. And huge they are with a capacity of 6000+ passengers. They do still have some smaller ships as well. My last cruise (March 2016) was on the Vision of the Seas, one of their smaller ships. What I remember was that the food was OK but not as good as I'm used of Princess and Celebrity. Entertainment was certainly better. RCCL certainly manages to attract people of all ages. The good thing about the big ships is that there's all kinds of things you can do and I like that most of these things are included with your price. This can be a positive point if you think your mother would make use of these.

Princess: I cruised with them last year in Alaska. I think you can compare them with RCCL when it comes to demographics. Their ships are smaller than those of RCCL and they have more staff compared to the number of passengers they carry. This results in a better service, we certainly noticed this in the main dining room. Quality of the food was also better than we had on the Vision of the seas. Biggest drawback of my Princess cruise last year was all the upselling they tried to do, you sometimes felt like you were walking on a market in Turkey.

Celebrity: When it comes to the cruise ships this is my first choice. I like their modern interior and they manage to deliver a slightly upscale product compared to the other cruise lines I mentioned in this post. The only reason I don't cruise with them all the time is that they tend to offer less interesting itineraries. Ship sizes and staffing is in line with Princess. Food I would say is the best of these 4 cruise lines (on par with HAL).

Holland America Line (HAL): They offer a somewhat more classical touch to the cruising. You will find more statues, marble, ... on the ship. Quality of the product I would say is on par with Celebrity.

These are my 5 cents. You should know however that another crew or another team in the kitchen can make a huge difference. Just have a look at cruisecritic.com and you will see how the experiences vary for 1 ship over a matter of weeks/months.

When choosing a cruise I tend to first look at the ports of call and not limit myself to a company directly. Honduras and Belize are nice spots for snorkeling which you might consider including in your cruise. Both RCCL and NCL (Norwegian) had cruises going there this year in March. (probably other cruise lines as well)

Make a shortlist of itineraries that look good, see what's in your budget and if you're not yet down to 1 cruise you can make a last selection based on the cruise line. As I mentioned earlier I wouldn't advice Carnival but the differences in between the 4 other cruise lines I mentioned are so small that they will not result in a hugely different experience, certainly not for a first cruise.