Turks/Caicos is a good option. Grace Bay is called the best beach in the world so your mom might like that. The water is that fantastic azure blue color also - pretty spectacular. Diving is all offshore - either locally off Provo's NW Point or better diving off West Caicos and French Cay (uninhabited) about a 45min. boat ride away. It's deep wall diving so lots of sharks, rays, turtles, cuda, all sorts of macro etc. Probably the best diving I've done in the past 5 years and I've been to most of the better Caribbean dive locations. It's pretty expensive there as Grace Bay attracts an upscale crowd.
There's 3 AI's there, Beaches, Club Med Turkoise or the Veranda. I've briefly been to Beaches - my recollection was of a lot of kids. Another option is Grand Turk, it's smaller, quieter and the cruise port. Bohio Dive Resort is located on the "best diving beach" in the world so that might suit both of you.
Beautiful by Nature - Turks and Caicos Islands - Turks and Caicos Tourist Board
Another equally expensive option might be Grand Cayman. Seven Mile Beach is an extremely nice beach and the dive operators will shuttle you to their boats from any of the properties along there. Some also have dive operators on site. Cayman diving is excellent as well off the wall Some of the dive operators will also pick you up off Seven Mile beach with a flat bottom boat.
The AI's there, Sunset House and Cobalt Coast are more isolated - esp. CC - and on ironshore - no beach unless you count the strip of sand that CC puts down - there's ironshore between it and the water. There's also a lot of condo options on SMB, vrbo.com lists many of them.
The East End is a lot quieter, Compass Point Dive Resort (condos)/Ocean Frontiers bundles packages in that area. The diving is supposed to be better - IDK about the quality of the beaches on the East End.
http://www.caymanislands.ky/default.aspx?homeredirect=true
Food is pretty pricey but some of the U.S. chains are downtown or along SMB so that helps with casual meals. The CI$ is fixed at .80 to the US$ so everything is 20% more. Boat dives are usually around 2/$100 also. One more affordable option is Comfort Suites, it's across the street from the beach, most units have small kitchenettes and Ambassador Divers is onsite - I recommnend them frequently.