You cannot file jointly because you are not legally married. You cannot claim her as dependents because she made more than $4050. She would not be required to file a tax return for less than $10,350 of W-2 income. However, if she did file a return and claimed the children, she would qualify for EIC and additional child tax credit for the children. You would not be eligible for any of those credits if you claimed the children as your dependents.
