How would the institution know it was funded with after tax dollars? Her preparer has "notified" the IRS over the years using Form 8606. Now you use Form 8606 with her return.
>>it is very vague on what expenses actually qualify.<<
The first section of the instructions to Form 2441 tell you to see Pub 503 for more details. Pub 503 says, "Expenses for a child in nursery school, pre-school, or similar programs for children below the level of kindergarten are expenses for care."
This is a forum for tax professionals who use ATX software for preparing returns for other people. From your question, I am guessing that you are using a do-it-yourself software for your own return. In entering your information into the tax program, you should not change the information provided on source documents such as W-2's or 1099's unless you are a professional and understand the consequences and meaning of such changes. So the short answer to your question is enter it just like you got it - do not mark it corrected.