At least through May 2010, the Radiance Of The Seas will not be going to Hawaii. The schedule only goes out that far.
As for ship age - the Radiance started cruising in 2001, so it isn't exactly newer in the world of cruise ships. It is the same age as the Golden Princess and just a little newer than the Zaandam. These two ships are with Princess Cruises and Holland America Line, respectively.
Larger doesn't mean the ship rides better. All modern cruise ships have stabilizers which are like the fins on a humpback whale. These are computer-controlled and are designed to reduce the motion of the vessel. There really isn't much difference in the ride between any modern cruise ships, and that includes the Radiance.
All cruise lines work with handicapped passengers to ensure they are comfortable and have mobility.
Here is a link
to Royal Caribbean's Accessibility Onboard page.
Here is a link
to Holland America's Accessible Travel page.
Princess doesn't have a dedicated webpage, but if you look here
about mid-way down you will find information on the award-winning PrincessAccess program. They also have a link to a service which provides beds, chairs, etc.
I suggest you look at these links and also call the numbers listed to get more details.
15 day cruises to Hawaii are not done on a frequent schedule by any cruise line. There are just a handful each year. I wouldn't become fixed on a particular ship or cruise line. Look at what you have to work with, such as the two excellent ships Neil mentioned, and start planning.
For some perspective, HAL is more formal than Princess. Also, a good rule to use with cruises is the longer they are, the older the passengers. On a 15-day cruise you will find mostly retired people since they are the only ones who can devote that much time to a cruise. Of course there are exceptions.