Take a look in the attachment. You can imagine that EncoderX and EncodeY are the values that comes from the wheels. (Here you have to move them by hand). On the plot you'll see the position in which the object can be found.
If it's a incremental encoder without reference you'll have to specify at the beginning the starting position.
2 .The other part with turning right and left:. I'm pretty sure that your wheel chair has an motion controller and a motor (connected to another wheel). That wheel (or whatever) cannot have too many axes. Probably just one. So the moving direction should be on the motion wheel direction. Thus, the direction is given by the set: [ (x[n-1],y[n-1]) and (x[n],y[n]) ] (high school mathematics). You can detect a turning when the direction changes (use a hysteresis in order to remove noise and inaccuracy).
In my example you should move all the time the cursors in order to see the direction. But I think you can get the idea.