I have ridden a LandRider, just because I had to try the centrifugal force derailleur system. I don't reccomend the bike, but will make a reccomendation for you and your wife.

--the Landrider is HEAVY. The "magical" derailleur is still a derailleur, but one that only shifts if you pedal quickly enough and smoothly enough. It is easily fouled by debris and dirt (and I'd suggest the folks they market to aren't much into maintenance other than from the end of a hose). In operation, the shifting is novel, but not better than what it competes against: internally geared hubs like the Sturmey Archer hubs we all grew up with (and which are still made and sold). The quality of the frame and components are quite low.



--I suggest you consider bikes with internally geared rear hubs, such as those bikes sold by Electra, Giant, Breezer and Specialized. They are usually marketed as "comfort" "town" or "cruiser" bikes, and will address several of your concerns:

...internally geared hubs are shifted by a thumb lever or twist grip on the handlebar and are foolproof. On a 3 speed, you pick 1, 2 or 3 and it works seamlessly, every time. No dragging chain, no derailleur, no confusion.
...internally geared bikes come with various types of brakes, either with hand levers or the old-fashioned coaster brake that you actuate by pedaling backwards. Very easy.
...the townie, cruiser and comfort bikes have stable, relaxed geometry very well suited for beginner, tentative or even klutzy riders, and for those just seeking to get low-level exercise and transport.