If he is not trying to claim the children he has absolutely NO reason to enter their SSN's on his tax return. And if he gets those SSN's and uses them on a tax return before YOU file, your own return will be rejected when you try to e-file. That would require you to file by mail, which takes much longer for the IRS to process.
Do you have any sort of court order that ordered you to file a Form 8332? IF you have such an order you may have to let him get the child tax credit. But be careful----there are some deadbeat dads out there who will mess up your tax return and your ability to claim your children.
Are you the custodial parent? Do you have an agreement with the other parent to allow the other parent to claim them--due to divorce or that you live apart and share custody? Did one of you sign a Form 8332?
If there is a signed 8332 then the custodial parent retains the right to file as Head of Household, get earned income credit and the childcare credit. The non-custodial parent gets the child tax credit for children under the age of 17.
As far as the IRS is concerned, the custodial parent is the one with whom the child spent the most nights during the tax year--at least 183 nights.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
