No, you cannot change or substitute social security numbers for your children even though someone else has decided to claim them as dependents.
As a way of background, the person who can claim a dependent child is generally the custodial parent. For tax filing purposes, the IRS adheres to federal laws for dependent deductions. In this regard, if you and for example your ex-spouse, file your respective returns and you each claim the same child, the dependency exemption reverts to the custodial parent.
If you are certain that you are the custodial parent, and are entitled to claim the children, you can go ahead and file your return with your children listed as dependents. If your return gets rejected because the other party filed before you and claimed the children, then you could file a paper return, claim your children, and include with your return any documentation you feel supports your claim. Be prepared to get additional requests for information from the IRS.
@Mrsroyal7
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