S.G.
I am a law student and I live in Austin (Tx).
1) If his lawyer doesn't want to lose his license, he would NEVER advise any client NOT to pay a court ordered mandated payment. No lawyer would be that stupid, so your stbe is lying to you about that and I would put that in writing, on record and address it in court.
2) absolutely it is in your favor and highly likely to be done correctly in court if you put his new employment information in the decree. and remember, the key words to use is "in your child's favor" not "my favor". okay? because the court will look at this as what is best for your son. what your ex is doing is trying to stick it to YOU, but really he is negatively impacting your son, and that is something you have to hold on to in writing, in court and with your lawyer. Make sure you use words and verbaige like "my son, my child, for him, for his needs"... not "me, I, for me, I need" etc.
3) A judge will always side with the child. If you have custody, that judge will side with the custodian of the child to ensure the child can thrive. If your stbe recently got a job then that means his income has increased which means he can help take better care of his child which means a judge will WANT that in the decree. In Texas, they don't mess around with that, I promise.
4) I am unsure who pays, but if your stbe is requesting that this be done in court, then HE PAYS. if you simply wanted this to be added to the decree but he wanted to pull this through court... then he's silly. he pays.