My DS6 (naturally ambi, but taught to be right handed) sees an OT for fine motor skill issues. She was very insistent ... that he use the same hand for all his fine motor skills.
Why? Does she have evidence for some kind of advantage to using only one hand or disadvantage for using both?
I'm mostly ambidextrous, but I do some things better with my right hand and some better with my left (others equal on both). I've always worked on being able to use both hands, after seeing kids in my class (and adults) effectively crippled because of a broken wrist, finger, hand, etc.
Just my two cents, with no information about your son's particular situation!
Val