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" I've read that the custodial parent has the right to allow or dis-allow the non-custodial parent to claim the children when filing taxes."
Not true. Unless the decree specifically states so, the parents each have alternating years.
The visiting parent's tax break for his alternating years is partially based on the child support he should be paying. If he is not paying it, then the custodial parent can ask the Court to modify the decree so she gets to claim the children in his year, but this is not automatic. She would have to file for this in court, and have it heard.
Ergo, this is possible, but not without a court hearing (unless he agrees in writing to forgo his claim this year, which I am guessing he is not likely to do).
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