Just a quick thought...
My son has vision problems and until he was about 6 we did not know if he was ambidextrous or what the issue was. He did things with both hands. Anything on the left side of his plate he ate with his left hand, anything on the right side of his plate, he ate with his right hand. Your kid very well may be ambidextrous, but in my son's case, he could not see past the midline (his nose). When looking with his left eye he couldn't see the stuff on the right and vice versa. Could he possibly have eye tracking problems? They can have perfect vision and still have eye problems that you can't see. My son went to vision therapy and although he can now see past the midline, he still uses both hands occasionally, just because that is the way he learned.