It's a great interactive puzzle either way. I imagine that making it more highly interactive would be a great way to help kids get better at spatial reasoning.
The undo button thing would be a huge improvement; I'll fix that. (Also, if you do two transformations that cancel each other out, it will notice and remove both rather than adding two. So you can actually undo a reflection by clicking the reflector again.)
As some other comments have pointed out, you might have seen the text based dilation, which is used for one of the problems for a specific reason :). The dragging dilation tool is far from perfect, but is a bit closer to what you described.
Consider this solution for the third puzzle of Transformation Puzzles 2:
Reflection over the line from (1.5,-1.5) to (-1.5,1.5)
Dilation of scale 256 about (2.5,2.5)
Reflection over the line from (1.5,-1.5) to (-1.5,1.5)
Dilation of scale 1/256 about (2.5,2.5)
Second, wow, a scale factor of 256! Off the top of my head it might be numerical error building up. If that's the case, I'm very sorry. (It's also sometimes possible to get infinitesimally close to the target without technically reaching it mathematically, in which case the interface unfortunately looks like the answer is correct, when it's not.)
All of the puzzles are solvable with dilations of scales only 2 or 1/2.
I ran into a situation where it seemed like there was no viable solution which kept the figure under manipulation within the visible bounds at all times, so it was made more difficult by having to visualize where it went offscreen in order to keep track of what I had to do next. It's entirely possible that I could refactor the operations into something that kept it onscreen the whole time, but I couldn't find it, so I really wanted a way to zoom out or pan around, or at least some encouragement like "this should be possible without the shape leaving the visible area." Maybe giving the user the ability to zoom out but also drawing a bounding box that shows the space you're expected to do the transformation in would help.