I have not read through this entire thread, as it is rather long. But I can tell you this.
When it comes to the dependents of separated or divorced parents the IRS has their own rules that must be followed. The only entity that can over ride those rules would be a federal judge. Since federal judges do not handle separations, divorces or child custody issues, I'm highly confident in saying that will never happen. A lower court judge can not over ride federal tax laws. Period. (Even though some state level and lower judges incorrectly believe they can.) But there is one thing a lower court judge can do.
Basically, federal tax law on this is covered in IRS Publication 504 at https://www.irs.gov/pub/irs-pdf/p504.pdf What will matter to you starts on page 11 of that document.
Basically, the IRS says, "The custodial parent is the parent with whom the child lived for the greater number of nights during the year. The other parent is the noncustodial parent."
Now what I lower court judge can do, is order the custodial parent (as defined by the IRS, not as defined by a lower court judge) to sign an IRS form 8332 giving the non-custodial parent the right to claim the child as a dependent on the non-custodial parent's tax return. If the custodial parent refuses to sign the 8332, then the court can hold the custodial parent in contempt of court. Even if the custodial parent still refuses to sign the 8332, the non-custodial parent just flat out can not claim the child. The IRS will not under any circumstances get involved in any legal proceedings concerning this either. The bottom line is, if the non-custodial parent does not have an IRS Form 8332 signed by the custodial parent, then the non-custodial parent can not claim the child. Period.
Now understand that even with a signed form 8332, the custodial parent can still claim the EIC for the child if they qualify and the non-custodial parent can not.
