Q:

Looking for bike trailer with pedals for a disabled, older adult

Is there a way to have a pull-along bike trailer w/pedals (similar to the child sized trailer in the pic above) -- but sized for a disabled adult?  

A:

Disabled cyclists are cyclists and so they would like some control over steering, braking, or pedaling. 
It's tough to design a strong singlewheeled adult-sized pedaled trailer because of the weight involved (50-200kg; 100-400lb) with adult riders. That's a lot of stress on the hinge-joint that connects the trailer as well as the front rider if  the rear rider doesn't have the ability to balance themselves. As a result, rear adult-sized trailers tend to be two wheeled and not pedaled, but this doesn't meet the requirements for pedaling (not to mention steering and braking). The same goes for designs where the disabled rider is carried in the front but has no control over steering/braking/pedaling. They are just passengers, not cyclists.

Trike pusher: One of the things that my adaptive cycling center does is use a regular recumbent or hand cycle  tricycle  for the disabled cyclist -- and attaches a regular upright cycle onto the rear as a pusher cycle, with a non disabled stoker. 
The design is simple. The pusher bicycle is a regular bicycle and take the front wheel off. Then get a truck-bed bike mount (the component in the middle) and mount it on the rear axle of the recumbent. Mount the pusher bike to the recumbent and voila, you have an easy way to create a recumbent tandem that allows a non-disabled cyclist and a disabled cyclist to ride together. The disabled cyclist in front doesn't have to pedal if they don't want to, but they do have control over steering and most of the braking power.

The advantage of this design is that at the end of the day, you can separate the two bikes which retain the ability to operate separately. This also makes storing and transport much easier. It works on adult tricycles as well as delta trikes. Tadpole trikes require a little more work (a solid rear rack).

Another option if you have the space is: have you considered getting a tandem or sociable? I ride a tandem recumbent tadpole trike as well as sociable quad at my local adaptive cycling center. Lots of fun for both riders, who can be of differing abilities and neither needs the ability to balance.
Finally, as I said, my adaptive cycling center places a tremendous amount of emphasis on the control and autonomy of the disabled cyclist. We actively reject the notion that getting passively pushed around in a wheelchair-rickshaw is cycling. 
If you google image "adaptive cycling tandem" you can get some other ideas. 

