Yes, if both of you claim your children, the IRS knows and will flag it. However, if their mother is not claiming them, there will be no issue.
I have been the custodial parent, and the non-custodial parent. I also know that if you can prove that you provide more than 1/2 of the child's support, that you are eligible to claim the child, unless a divorce decree states otherwise.
Good luck on your taxes... although given the time of this question - you have probably already filed.