As silly as it sounds, if you are the primary, and your child does not wish to have his hair cut, get a court order.
Your ex sounds like he has issues with power and control. (so does mine) I had to go back and state who does what in our custody decree. Silly, but when you are dealing with a newly born again, power freak I had to take it to the court. My former spouse is law enforcement, every time we disagreed about something, he would threaten me with jail if I did not do what he wanted. I finally got that on tape, and took him to court. Now, I have sole custody, and if he were to do something that is not within his "parental rights" (like a haircut, ear piercing, hair dye, taking or rather NOT taking the children to the Dr) he is in contempt of court and it costs him in his wallet.
I had to do this, but not all relationships are this evil. Try going to couples counseling, or " child couseling." I wish that had worked for us, as I hate having to get the authorities involved.