I work with the AARP program in PA. A couple of years ago, I had a return that was rejected on the last day, and had to be mailed in because it couldn't be efiled. I was told to have a copy of my rejection notice included with the mailed return and all would be ok and it wouldn't be considered late - and it did work out OK, with no penalties for the person whose return it was. I think there was a time limit to send it in, just a few days or maybe a week, but I don't remember for sure. But you need to get this sorted out quickly.
As someone said above, TaxAide sites are closed now, but most of the volunteers still take calls at home - I do, as well as the people I work with. We're not done until all loose ends are tied up.
Call the person who prepared your return and ask them for a copy of the rejection notice, and include it when you mail your return, along with a note from you explaining the situation. You'll probably be OK and not have to pay penalties or interest. If you can't get the copy of the reject notice, a note would probably end up being enough.
Your state return might or might not have gone through. For what we use, if the federal rejects, the state doesn't get filed either - since it's the same program, that might be the case for yours too. Ask the person who prepared your return.
Your daughter will have to amend her return dropping her claim to her own exemption - and if that makes her owe taxes, she'd have to pay them, but it probably wouldn't matter so she probably won't owe anything. The people who did her return actually should prepare the amendment without charging for it - they sure should have asked, knowing that she was only 15, whether she could be claimed as a dependent. But you don't HAVE TO have them do the amendment.
If your daughter doesn't amend her return, you'll both end up dealing with some more IRS paperwork trying to sort out who has the right to the exemption.
Good luck. Many of the AARP volunteers would help guide you through fixing this.
If you have any questions, feel free to email me - see my profile to send an email.