Had this happen to me when my wife lost her best shots of her favourite day of our recent Scottish trip whilst she was putting them on the iPad. It was my iPad so I was in big trouble - if you are married you will understand how that works!
There is no way for mere mortals to recover trashed files on the iPad as the Trash is not visible, something to do with sandboxing but not worth discussion, you can't get to it.
However, googling 'Mac recover lost files SD card' brought up a lot ot programs and there are a few on the App store. One I tried did nothing, then the next - named something like 'Data Recover US' but longer - showed the missing files, dragged them onto the desktop and showed them in a slideshow and you could feel the tension level in the house dropping. It was free and if you are on a PC I am sure you will find similar programs.
All is not lost, good luck.