My ex-wife will not let me claim children for ta

Your first step would be to file a Motion for Contempt against your ex for violating the Court Order. At the hearing on this, the Judge will (or should if asked) require her to produce the children's  social security numbers. A lawyer can assist you with getting that Motion filed, and other documents that should be filed, as well, in order to show the Court that you are asking her to produce her tax records for a certain number of years, social security cards, etc.  Have you made contact with the Social Security Administration with a copy of your divorce paperwork to see if they will make this information available to you?   Hope this helps.