You mention your mom being "wheelchair bound" so I am assuming she's a full-time wheelchair user and not just using one to replace distance walking. I would suggest that you work with a travel agent who is a disabled travel specialist. They would be able to set up accessible tours in San Juan, St. Thomas and Grand Cayman if your mom is a full-time power chair or manual chair user who doesn't have the upper body strength to do a lateral transfer into a cab. If your mom uses a manual chair AND can do a lateral transfer, you can use cabs for transportation and/or tours.
For a full-time wheelchair user, I agree with the member who suggested Royal Caribbean, Celebrity and Princess.
Because you used the term "mum", I'm assuming there's a good chance you're writing from the UK. There are a few disabled travel specialists in the US and a couple in the UK. I don't know if this is true, but I recently was told that the disabled travel specialists in the UK add very hefty fees. If I'm right and you're in the UK and you find that there are extremely high fees, I would suggest contacting a US specialist who can easily work with you "from this side of the pond." <g>