Hello, There are several issues here.
Your wife cannot 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 separated parents: http://www.irs.gov/publications/p503/ar02.html#d0e751
Essentially those people who your wife allowed to claim the children must have:
- Provided for more than half the support
- Lived with the child in their same household for a majority of the year
- Not been the qualifying child of anyone else.
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 please 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 agreement to allow for you to claim the children. Make sure you use IRS evidence of who is claiming the children.