I posted in the other thread and you need to refer to IRS publication 501:
https://www.irs.gov/publications/p501
The bottom line is the parent with custody has the right to claim the children as far as the IRS is concerned for divorces after 2009 unless you have a signed Form 8332. Do you? If your divorce decree says you are entitled to claim them you need to get that form signed. If your decree is silent regarding claiming the children your lawyer probably screwed up big time, especially since the value of claiming them was known at the time of your divorce since the new tax law was in effect.