Yes---if you are the custodial parent, then claim your children on your own tax return. You will not be able to e-file if the other parent filed first and claimed them, so mail your tax return. The IRS will sort out which parent could claim the children. If the parent who claimed them first did so incorrectly or fraudulently, he will be subject to repaying any child-related credits received and penalties.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as certified mail so you will know the IRS/state received the return.