If the return is rejected because the social security numbers of your dependents has already been shown on another return, you may still be able to claim them as your dependents.
You will not be able to e-file claiming your dependents - you will need to file a paper return, which take considerably longer for the IRS to process (generally 4 - 6 weeks).
The IRS will eventually contact both of you to figure out who gets to claim the dependents. The losing party will then be liable for any additional taxes, penalties, and/or interest as a result of the false claim. Because the IRS will need to make a determination as to who can legitimately claim the dependents (after they have contacted both of you and have received a response from both of you), this process can take a considerable amount of time.
