Based on the information you provided -- and the recording of the IRS interactive interview, which was very helpful -- it certainly seems that the second child should only be eligible for the Credit for Other Dependents, as you suggest.
One thing before the next step, though. As you say, your child shouldn't be getting the $2,000 credit, since he has an ITIN. As described in What is an ITIN? in the IRS' Publication 4757, Individual Taxpayer Identification Number (ITIN), the IRS has a certain range of numbers that are reserved for ITINs:
All valid ITINs are a nine-digit number in the same format as the SSN (9XX-8X-XXXX), begins with a “9”and the 4th and 5th digits range from 50 to 65, 70 to 88, 90 to 92, and 94 to 99.
If your child's identifying number doesn't fall within these ranges, you should check with the Social Security Administration to make sure your child has the correct identifying number.
That said, if your child actually does have an ITIN rather than an SSN, and you're still not able to get the Credit for Other Dependents to generate for him, use the workaround below.
Indicate in the TurboTax interview that this child is "other" (not child), and then indicate he's a legal resident, and lived with you the entire year. This will then list the child and check the box for "other dependent," awarding the appropriate $500 credit.
Do not be concerned that you are perjuring yourself by making these entries. These are TurboTax entries only, and aren't questions on your actual tax return that you'll be answering wrong. These are merely answers that will get the return to provide the proper information to generate the correct credit.
