Q: My wife deleted my notes files and they are not backed up on icloud.  Is there a way to recover it.

Notes usually sync with mail accounts- try to sign in online if all accounts that you see when your open notes app and click accounts. Especially in the one that you find when you go to Settings- notes- default accounts. With most accounts sync works one way so when you created notes they were uploaded to mail server and then when deleted on the phone still stay inside of notes folder of your mail server. If your default was icloud notes, they do support two way sync and that means - nothing you can do. Especially if there is no backup.