Why can't you make sharp edges after a curve with the pen tool? Or can you?
I did this curve...
And I just clicked, one time, and I got this...
The red line is what I want to see (another curve), but it looks like it just can't happen. I tried double-clicking, but that didn't work. Or did I do that right?
simply click the anchor point again, then continue to draw. This will create a "cusp" -- a point that has a curve on one side and a corner on the other.
Simply draw the curve that you require with the pen tool. Then without letting go of the mouse hold then 'alt' key. This gives you independent control of the control handle. You can now draw straight corners.