Can EAGLE CAD make square-ended traces?
I've done this two ways:

Position the wide trace's endpoint somewhere on the upper edge, not the middle, of the horizontal trace.  Then use a narrower trace to make a connection from the wide trace's endpoint to the midline of the horizontal trace.  The narrow connecting trace will be surrounded by copper, and so it's only there to make Eagle happy.
Or,

Draw the wide trace as you have it shown in your second image.  Then, draw a polygon over the top of the wide trace, using the edges of the trace as guides.  Of course, don't draw the extended radius in the polygon :)  Assign the polygon to the same net name, then delete the original trace.


I can add pictures later today if this doesn't make sense. Please let me know.