I think double clicking may be confusing, so I suggest a simpler solution instead. Clicking within the mini-rectangle on the toolbar would trigger selection of all borders:
I have also added some tooltips while hovering over the borders or the center of the rectangle. I don't think presenting the style of the borders within this mini-rectangle is a good idea - it will be visible in the canvas anyway, and presenting it on toolbar leads to clutter, methinks. Anyway - the one on the toolbar is just a simplification - in fact it is a square, so it does not reflect the actual shape (aspect ratio) of the rectangle.
Regarding tooltips - I think you should provide them for other tools as well. You can also consider adding a small triangle down next to style and color to indicate that these trigger a list of available options.
In the same time, you could consider providing some other control for the roundness, which - I believe - is more corner attribute than border attribute. Of course you could control both corners, but in this case what would happen if you change roundness while modifying right border and then switch to top border and modify it again? They share a corner, thus roundness of corners should be separated from border adjustments.