It does sound like a collection of bugs.
Not sure an #image inside an #exercise inside a #sidebyside has been considered.
First question, the @width is relative to what?
(In a "normal" #sidebyside we assume an #image consumes the whole panel.)
A #sidebyside in a #worksheet, holding #exercise is a really different thing. It is meant to be a convenience for authors, to recycle it as a language for layout control. Perhaps we should identify #sidebyside in the pre-processor - normal, worksheet, interactive - and react accordingly.
When you have a MWE, or a free minute, it'll be interesting to see what LaTeX does with this.
Rob