There is no one that you would technically contact to stop your wife from claiming your child. Basically, what it comes down to is who did the child live with for more than 6 months out of the year. If they lived with you, then you will just need to file your return and include them on your return. If your wife happens to file first and claim them first, you will need to mail in your return and the IRS will use the Tie Breaker Rules to determine who gets to claim them.
This will make it take longer to process your return, as the IRS will then reach out to both of you to determine who is "telling the truth" and who gets to claim them. So if you do end up needing to mail the return, you may want to include a letter stating attachment to return with a copy of your custody agreement or proof that the child has lived with your over 6 months during the year such as school enrollment, daycare, etc. This may or may not help speed up the process, as they may or may not pay attention and send you a letter requesting proof anyways.
If in the end, your wife erroneously claimed them, then your return will be processed with the child on the return and your wife would have to pay back any refund she received that she was not entitled to.
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