When you get a letter adjudicating a claim against you, you should begin taking steps to respond
immediately. "Taking steps" could involve some preliminary research, such as to find out any limitation periods that may apply. In any case, you certainly should not lose the letter.
In terms of just getting a copy of the letter, you can certainly do that using the IRS's Freedom of Information process:
http://www.irs.gov/uac/IRS-Freedom-of-InformationWithout actually seeing the letter, we can't say for sure what was really contained within, which would be relevant to any limitation periods.
That said, it looks like you could potentially still be within the limitations period to challenge the adjustment to your tax return. According to 26 USC § 6511, a claim for a refund of overpaid tax must be filed by the later of (i) 3 years from the time the return was filed, and (ii) 2 years from the time the tax was paid.
Since your complaint is with the 2013 tax year, you filed your 2013 tax return no earlier than January 1, 2014. That means you have until at least January 1, 2017 to file a claim for overpaid tax in respect of that year.
In your shoes, I would do the following:
1. Obtain a copy of the letter using the FOIA process. This is mostly for your records and is probably not necessary for the next steps. You probably do not need to wait to receive it before moving on to the next steps. You can perhaps even skip this step.
2. Obtain a tax transcript for the tax year 2013. This will show you the changes that the IRS made to your return for the year 2013.
3. File an amended return for 2013 on Form 1040X where you again claim two children and request a refund based on same. Include the evidence that you have two children.
