BBM I have not seen anything that says, for a concrete fact, that J was sent away. The only think I have read anywhere close to that in an actual news report (paraphrasing because I don't know the link) the J and Kaine had been butting heads. It DID NOT say KH or TH sent him away. It DID NOT say KH insisted he be sent away; but, that is what a lot of people have decided to "read into it". The article also stated that J's grades were slipping and it was in his best interest to move.
FWIW, I agree w/ you that this may or may not have anything to do w/ this. It could have been that Kaine got tired of butting heads OR it could very well have been that Terri got sick of the butting of heads. Perhaps she felt she had to much on her w/ the baby and Kyron to put up w/ behavioral issues, step parent issues, slipping grades, loss of control over J, etc.
Let me note that it could also very well be that TERRI used the excuse of butting heads and slipping grades to send J off once she decided to pursue the murder for hire plot. One less person to be watching her or overhearing something. It would also keep him out of danger if the plot had succeeded.
We just do not know. Now, if anyone else has seen anything I missed, please correct me.