to get the credit a married couple must file a joint return. the only exception to this is if all these tests are met
1) the taxpayer paid more than 1/2 the cost of keeping up the home for the year
2) the spouses lived apart during the last six months of the year
based on your post both of you would fail the last test and the lower income would probably fail the first
so you can file separately but neither of you would qualify for the credit.