There are several issues here.
Your wife can not legally allow someone who is not entitled to claim the children to do so. IN order to claim your children, the children must meet the qualifying child or qualifying persons or relative tests.
Those tests can be found at this link:
1. Qualifying persons: http://www.irs.gov/publications/p503/ar02.html#d0e257
2. child of divorced and seperated parents: http://www.irs.gov/publications/p503/ar02.html#d0e751
essentially those peopel who your wife allowed to claim the children must have:
Now for you:
The IRS rules state that the person with whom the child lived a majority of the year is the custodial parent and can claim the child including all of the other entitlements.
However there are two exceptions.
1. If she signs a form 8332 allowing the non-custodial parent to claim the child.
2. If the divorce decree states that the non-custodial parent can claim the child.
Now I do not know how you know that persons not authorized to claim the children did so, and pleas do not tell me. But, you can report the ones who claimed them to the IRS fraud line, and you can report the mother because she enabled them.
What you need to do is to ask her to sign the form 8332 for you (even if you have to agree to share the return): http://www.irs.gov/pub/irs-pdf/f8332.pdf
Then you need to leverage that by going back into court and asking for a modification and or rearrangement to the divorce decree and custody agreemetn to allow for you to claim the children. Make sure you use IRS evidence of who is claiming the children.
Since you were never married, the only difference is that you do not have a divorce decree.
My answer remains the same, except that you still need to modify the court order for custody to address the issue of taxes.
Here is the IRS treatment of your question:
If you pay child support, are you allowed to deduct anything on your taxes or claim the child as an exemption?
Nothing can be deducted for the child support payments. Child support payments are neither deductible by the payer nor taxable income to the payee. You may be able to claim the child as a dependent. The parent who the child lived with for the greater part of the year is the custodial parent. Generally the custodial parent is allowed to claim the exemption for the child if the other exemption tests are met. However, the noncustodial parent may be allowed to claim the exemption for the child if the custodial parent signs a Form 8332 (PDF), Release of Claim to Exemption for Child of Divorced of Separated Parents, or a substantially similar statement.