I would suggest that you carefully review the court order concerning the custody/support of the children -- all that I have seen and been involved with specifically address which parent is to claim which (or all) child/ren ---some agreements will split the children (one to you/one to ex) or will grant that the parents claim them on alternating years or will grant that one parent (typically the custodial) claim them at all times. Although the NCP is sometimes required - as you are- to carry medical coverage and pay support the amount you pay is not in truth enough to fit the legal definition of a dependant used to determine someones right to claim (for tax purposes a dependant is someone for whom you contribute more than 50% of upkeep costs for the 12 month period of that tax year)....child suppport may seem high, but in most cases the amount of support paid does not actually equal half of what it takes to support that child for that year.
If you do not find the issue is addressed in your order (as it was apparently several years ago it is before my becoming involved in such issues so my knowledge may not extend that far back) I suggest you contact your lawyer and inquire with them....if you are interested in claiming one or both children you can petition the courts for an amendment that would allow such a claim but I have to warn you that it would be difficult to attain and likely only cost you $ and headache.
Good luck and God Bless
