Well, you can't stop her from committing fraud. About all you can do is warn her and perhaps alert the IRS. If the kids ss# show up on your return and hers eventually the IRS will cross-match the returns and investigate. I would try to file your return as soon as you possibly can and make sure it is done right by using a CPA. This will be investigated so keep your documentation and paper trail.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature. Visit Steve Zelinger's website: http://www.stevenzelinger.com/
File your return as you normally would, and be prepared to show they live with you. The school records are great. They establish that the child lives near the school for more than half of the year.
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As Steven suggested, you can't stop someone else from doing something unwise. If you're in the right, just keep a good paper trail by retaining all pertinent documents, and if your return gets examined then it is simply a matter of calmly and coolly presenting your evidence.
Best of luck
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