Two points I want to emphasize.
1. You must have there SSNs before you file. If you can't work this situation out by April 15, you need to obtain an extension.
2. While you might be qualified to claim the grandchildren as dependents, their mother probably has a superior claim. If she files a tax return for any reason, she can claim the children ahead of you, because she is the parent. (Even if your income is higher than your daughter and even if you provided most of the family support.) She might get less tax benefit than you, but that can only be tested by comparing different scenarios. There is nothing you can do on your tax return to force her to let you claim the grandchildren. As you indicate, it is a matter for the local family court. However, is $4000 really worth it?
