if the one claiming you and the kids files first, your return will be rejected. you will then need to file by mail.
if it's theirs that's rejected, they can do the same file by mail
then the IRS will have two returns with the same SSNs. eventually, it will send out a letter to both parties asking the taxpayers to amend. if neither does a second letter goes out to both parties asking for proof.
those second letters will contain info as to what to use as proof - things like doctor bills, school records, pictures of the kids bedroom with pictures of the kids in them, affidavits from neighbors, etc. the IRS then decides who submitted the best proof. the other gets a bill.
