I have a new neighbor with a really cool 10 year old daughter, and they are looking for a special trike for her. Or maybe a bike. Her difficulty is that she has only one arm and one leg. They got her a delta trike about a month ago that has rear wheel steering and a coaster front hub. It works good for her, and she can go pretty fast for short bursts on it with a pedal cadence over 100, but she really wants something with some gears where she can keep up on neighborhood rides. The limitation on her rig is it’s basically a direct drive 16” wheel with short cranks.  
Anybody got any ideas on what they ought to look for? My first thought was a small cattrike, but brake steer would be a big problem with that unless someone knows how to make it actuate both brakes from one brake lever. Maybe a kid sized two wheeler bent with training wheels would be better, but I’d want it to roll nice. Any suggestions that won’t break the bank?

The WindCheetah uses joystick steering with a single lever controlling the brakes, which is a good solution to a problem like this.  Unfortunately, its not cheap or particularly available.  But it could be a model for a fabrication job.  KMX makes a child-size recumbent trike--still not cheap, if you you can find one.  Lots has changed in the last two years.

Three good ideas, thanks gents!