It may be beneficial to file a joint return with your wife which then allows the children to be claimed on the joint return. Note that there are some things that will not be allowed such as Earned Income Credit (since the children did not live with you in the US) but this may not be of concern.
To file jointly with your spouse, you attach a statement to your paper-filed tax return signed by each of you indicating that you wish to elect to treat her as a resident for tax purposes. You would need to report her worldwide income, but that income may be eligible for foreign tax credits or for exclusion under the Foreign Earned Income Exclusion.
You would need to weigh the benefits of filing jointly with the need to report her income as well as yours on the tax return.
There are other items to consider when making this election as well, including that it is a once in a lifetime election. You can learn more about it HERE.
If your spouse does not already have a Social Security number (SSN) or Individual Taxpayer Identification Number (ITIN) you will attach the application for an ITIN to the return and send it along with supporting documents to the Form W-7 processing center. If your wife has a pending application for SSN, it is better to file an extension and wait for the SSN to file the return, however.
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