When you printed your return, did you print it from the Tax Home page?
I'm guessing so, as that's what any logical person would do.
...but here's the rub: The TurboTax website is set up in two parts - the front end which is home to Tax Home, Intuit Account, the landing pages, and all that, and the tax software itself.
You'll notice whenever you click "Take me to my return" or "Pick up where I left off" or even just begin your account you go past a blue/green page. That page signifies you're leaving the front end and getting into the software itself.
The front end stores info that was submitted the first time, which is why if you print from there, you're seeing the bad SSN.
If you go past the blue screen (you can do this by starting on Tax Home, finding My Returns & Documents, clicking Show to expand the section, and then clicking "Add a State" on the Tax Home page down beneath the images of the US and your state) you can print from the Print Center in the sidebar under the Tax Tools tab, and you'll get the updated/ current version of the forms.
All that being said, when you get rejected, you should be getting an explanation why and a link to fix it. Are you sure it was your child's SSN? Is it possible someone else claimed the child? I see those happen quite often.