You have a J-1 Visa and are filing a Federal 1040 as a Resident Alien. Your wife has a Social Security number and your daughter has an ITIN and have both have J-2 Visas.
Please see page 11 of IRS Publication 501. Towards the top of the page you read this:
“You can't claim a person as a dependent unless that person is a U.S. citizen, U.S. resident alien, U.S. national, or a resident of Canada or Mexico.”
If you meet the requirements listed in either of the two columns on page 11, Tests to be a Qualifying Child, left, and Tests to be a Qualifying Relative, right), you will be able to claim your daughter as a qualifying child or a qualifying relative on a Federal 1040.
However, you will not be able to claim the Child Tax Credit or the Earned Income Tax Credit for a child with an ITIN.
See this IRS publication.
“If a primary taxpayer, spouse, or both have ITINs, they are ineligible to receive the Earned Income Tax Credit (EITC), even if their dependents have valid SSNs. If the taxpayer and spouse (if filing jointly) have valid SSNs, only dependents with valid SSNs – not ITINs – qualify to receive EITC.”
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