You could put some of the non-slip tape on the bottom of your ruler to help stabilize it.
When I sew my corner pieces, I usually sew one needle width inside the line (toward the corner). When I sew right on the line, by the time I press, sometimes the corner bits are too short. I also leave the big square underneath intakt and only trim off the triangle piece. That way I align my sewing line on one big piece.