@AlleyOmalley -
he is correct, that your roommate can not claim your children for EITC because there is no legal or biological relationship between them and her.
https://www.irs.gov/credits-deductions/individuals/earned-income-tax-credit/who-qualifies-for-the-ea...
However, it is possible for your room mate to claim your children as a dependent since they lived with her all year. best to review this calculator to determine for sure.
https://www.irs.gov/help/ita/whom-may-i-claim-as-a-dependent
note there is one credit for dependents and a separate credit for EITC. the roommate can't claim the children for EITC but may be able to claim them for the 'other depedent credit'
