Unfortunately, the only way you will find out if someone has truly filed a tax return with your dependent child listed on their return is when your e-file is rejected, or if you submitted a paper return, you receive a letter from the IRS advising your child was claimed on another return. The other party will receive the same letter as well.
These letters will eventually require both parties to provide proof they supported and have the legal right to claim the dependent on their return.
Hope this helps.
