Thank you, pk, for getting back to me!
The visa I have is O1, and my family members have O3. We arrived from Israel.
Per the IRS, my kids are not considered dependants and were rejected from ITIN because they were listed in my return without being claimed for allowable tax benefits. This sounds very weird as they are 6 to 12 years old, living with us, and no one is helping with their expenses.
PS
For my wife, they approved the ITIN
