I iron my bindings in half. Never had a problem, so I suppose I will continue to do that.
I trim the bulk of the extra batting and back, just so it is out of my way, leaving about an inch. Then sew the binding onto the quilt top with the 1/4 in. seam. We don't want to lose points. Leave that extra batt and back on.
When I come to a corner, I stop 1/4 inch from the edge of the quilt top, sew into the corner on the 45º angle, and LEAVE THE NEEDLE DOWN at the tip of the corner. That little extra batt and back will hold the quilt at the needle. Turn the quilt to sew the other side and PINCH the binding to form that fold at the corner. Lay the fold down so the edges are in the correct spots. Then lift the needle, move over to the sewing line and start sewing. No taking the quilt out of the machine, no starting a new line of sewing (with the possibility of thread nests).
After the binding is sewn on, lay the ruler on and trim to desired width with a rotary cutter. Do short segments at a time. You will be far enough away so you won't cut into the folds at the corners.
I have seen one quilt that actually had piping rope inserted into the binding to make a fat edge. Looked fine.