I'm sorry that your W and child are banned from the gym for a week. Children can act out w/either parent. If I read correctly, your son is 4. Some children do act out and bite and pinch others. I know that my nephew (age 2) went thru this phase and he was in a loving home w/two parents and had a thing for chomping on his father's calf and he didn't do it out of meanness, but wanted to see how it tasted. It could be that another child took a toy away from him, he could have been hit, pinched, pushed or bitten by another child. At that age, they are most likely defending themselves...but I definitely would ask about it. I seriously doubt that your W was paying attention to the situation because the child was probably in the day care part of the gym and the person who saw the incident should be able to tell you or your wife what happened. When your son is w/you, you can gently ask him about it and maybe he can share a bit of light on it. Then you can gently tell him that it's not the proper thing to do if someone is bothering him.
Also, if your child is in day care, someone may have bitten him and he's not picked up that bad habit as a way of defending himself and/or "standing up" for himself w/other children. It is worth investigating because you do not want him to go to pre-k biting others. If he were younger, I would say it's an experimental behavior to see how things taste and feel in his mouth, but at the age of 4, he shouldn't be doing this. I suspect he was provoked by another child...