what is happening with the corner that "doesn't come out right"? Have you checked your seam allowance both for coming into the corner as well as the next seam. How far did you come down to the end of the eam. Stop a couple stitches before you come to the seam allowance at the corner. this will leave a bit of space for the fold in your binding.
Usually the reason for corner not coming out right is irregular seam allowance. Also make sure the fold is exact 45 degree angle hwn you fold for the next seam.
I usually don't trim the corner. However, sometime just take a small clip at the corner. If for some reason the corner is too bulky with batting I will shave a bit of binding out.
I don't clip much at the corner.