I'm working on a PhD in School Psychology, so this thread is very interesting to me since it's probably something I'll have to deal with in my future professional life.
1) Right or wrong, teachers can have fragile egos and don't like to be told how to run their classrooms. Heck, HUMANS frequently don't like to be told how to do their jobs!
If I were you, I'd take out anything in the letter than sounds accusatory and restate it as "Huh, don't know why this isn't working, but it isn't. Together, let's identify barriers and see what we can do to solve those problems." Stress working together instead of "I'm pulling my weight, but you're not." Other posters hit the nail on the head when they said that teachers have A LOT of students to worry about and may not be able to keep up with individual plans for each student.
2) I agree with the other poster who suggested that you get someone in administration involved, whether it's a principal, a school counselor, or a school psychologist. The counselors/psychologists have been trained to deal with things like this and can be a big help.
Perhaps, if his dad would reinforce my efforts while my son was there it would not be necessary to use this as an incentive. Or maybe it would just mean that Dad's house isn't so fun that it can be used as both a punishment and a reward. Either way, this is the ONE thing that has motivated him to follow through with anything. And he keeps track of it and gets excited when he has almost earned an extra day with Dad. I think that's great. Whatever it takes to get him on the right track. This isn't some kind of evil game I am playing or trying to keep him away from his Dad. It's me trying to create an environment in which he is motivated to succeed.
3) The most important thing I learned in my Behavior Management class is that it's more effective to focus on good behavior than bad, i.e., focus on reinforcement instead of punishment. This would help alleviate the perception of mom's house being a House of Pain and dad's a House of Fun, especially
since his dad isn't on board with anything that puts him (dad) in the Bad Guy role.
Make everything a privilege to be earned -- watching TV, playing video games, spending time with friends, and anything else your son enjoys (besides feeding, clothing, and housing him). With each chore completed, each assignment done, he earns some privilege, e.g., 2 hours of TV time, 1 hour of video games, etc. Think of things that your son finds motivating and be creative! Extra time with dad (if dad's available for that), NOT having to do chores (e.g., if you do dishes 5 days in a row, you get 2 days off. If not, you have to do all 7), etc. So it's not a matter of suffering through punishments until he can escape to dad's, but that through his responsible behavior, he gets to do the things he wants to do.
To start, make things easy and have tasks be in small chunks. You don't want to say something like, "If you do EVERY assignment EVERY day for a month, you get XYZ reinforcer." What happens if he screws up on Day 3? No motivation to stick it out for the rest of the month -- he's already blown it. So each DAY of all assignments done earns XYZ reinforcer. Make sense? Set reasonable expectations/goals that build in him a sense of confidence and competence.
And, if I may, I highly recommend that you watch the ABC show Supernanny. I got hooked when my professor showed us clips in Behavior Management -- Jo (Supernanny) demonstrates a lot of what I'm talking about -- focusing on the positive, reinforcing/rewarding good behavior with rewards that are motivating to the children, etc.