It would help to know what specific test they think you did not meet, so you can tackle that specifically. Do they think your children did not live in your home? Do they think the children are not disabled? That you didn't pay the household expenses?
Here is a letter The IRS uses to request proof to verify EIC claims. These same proofs will apply to the dependent and residency tests for HOH status. https://www.eitc.irs.gov/eitc/files/downloads/f886_h-EIC_2012.pdf
