My daughter was arrested for dwi. She entered a program that required she take a coursr and do community service. She has successfully completed all that was required of her but she still can work in the teaching profe3ssion as the arrest appears on a fingerprint test

Some issues,

First a fingerprint is not a test, it is a check of Identity. All fingerprints do , is be sent in and verify if that person has ever been fingerprinted under another name. It gives a positive ID of that person.

Then, after they have been positively ID'ed, they run a criminal records check, or other check, (for credit, for immigration, for domestic violence record and so on.) in the US, the national criminal back ground check is known as NCIC records check. This would be done, after ID has been verified by finger printing.

You can have your own record ran, ( pay for it) and see what shows up.
Your attorney can check though courts to be sure that this record was explunged.
The record is never actually deleted, merely marked to show that no conviction was done, and that it was cleared though a pre conviction program.
Depending on what record check is completed what will show up.