You may claim your granddaughters as long as the following rules
can all be met:
1. They are under the age of 19 or under the age of 24 and a full time student.
2. They lived in your home for more than half of the year.
3. The children did not provide for more than half of their own support.
4. They are not the qualifying children of another taxpayer
If they did not live with the maternal grandmother for more than half of the year, then you are the one with the right to claim the children.
If she also claims them on her return, you should go ahead and file your return and claim the children. If she files before you do, then you will not be able to e-file your return as it would be rejected, because it would show that those dependents had already been claimed by someone else. In that case you will need to mail a paper return. Attach a statement to your return that states all the facts (as shown above) that explains why you are entitled to claim them.
The IRS would then notify the other grandparent, and request proof from them of why they are claiming the child. If she cannot prove the children lived with her, the IRS would disallow her deductions
and let you keep the exemptions.
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