A business loss will reduce your other taxable income and your tax liability. You must have enough income to have a tax liability in order to take either one of those credits. Unless there is a tax liability there is nothing that the credits can reduce.
Preview your 1040. Go to My Account >>> Tools >>> Tax Summary >>> Preview 1040. Look at line 47. This is your tax liability; if it is 0, you are ineligible for the credits.
Furthermore, in order to receive the Additional Child Tax Credit, you would need to have at least $3,000 of earned income. This includes wages from the two of you and your business loss. Check line 37; if under $3,000, the Additional Child Tax Credit is unavailable to you also.
