I've run into problems like this in the past. You can attach extra pages to the return explaining the situation. Believe it or not, it works. I would acknowledge that you claim the erroneous W-2 as your child's, and also explain what's wrong with the SSN, as well as the employer's stance. You might even include their communication to you stating that they won't fix it.
This looks like a good page to help you out:
https://ttlc.intuit.com/community/after-you-file/discussion/how-do-i-attach-an-explanatory-statement...
