He's a kid and he will do dumb stuff on and off the field. It happens and the vast majority of us have been through this. What matters the most is how you handle it once it happens. I have no idea what his attitude is or what off the field things he has done but those are your words. Right now based on what I'm reading, and I could be wrong because I truly have no idea what the whole story is, your son needs to have his first "man up" session and talk to the coach. The coach may be the biggest jacka$$ on the face of the earth but he's still the coach and he still makes the line up out. When you have an issue with someone the worst thing you can do is ignore it or run away from it - you face it. Have your son have a private sit down with the coach and see what's going on. Your son needs to be humble enough that if it's truly his fault to be wise enough to see this and work to resolve it. If it's not his fault then you will see that the coach is a jacka$$ and there's no resolving the situation. The good thing about this is you know now what's going on and can move forward.
The worst thing you can do is move because you're teaching your son to run from issues. You and his father are not letting him experience things to where he can learn, grow and mature into someone who can handle their own issues. You and the father can help your son do this by helping him prepare for the conversation. Go over things to ask / discuss, how to phrase things without having attitude and things like that.
Another issue with transferring him to another school is research the heck out of it. I'm assuming you and the father are not married and that you have primary custody of your son. Most states (if not all - not sure) will want the father to take over primary custody of the son before he's able to enroll or be eligible to play sports. As an AD myself these are things I have to look into when a new kid transfers into our school. Usually it's taken care of by our counseling department because our county does not allow students to enroll unless custody has changed hands. I have no clue what your situation is but it is something to think about.