Hello NancyDrew ... oh dear ...
If these are your only copy and you really want to retrieve them then STOP using the computer AND the Ext HD. Take them immediately to wherever is near to you that can recover the files.
Have you tried a Spotlight search of both the internal & ext drives? Do you think you trashed the folder or it's just gone off the radar?
If they wen't to the Trash while the Ext drive was connected and you then disconnected the Ext drive without emptying the Trash, then you wouldn't be able to find them on your internal drive - if you connected the Ext drive back up to your Mac ... well, the folder would appear in your Mac's Trash ... does that make sense?
What happens when files are deleted (meaning the Trash has been emptied) is that the path to the original location is lost (regarding from a search point of view) and their original file name is stripped away and these files just sit on your HD waiting for the System to write over them.
So, the quickest way to go is to stop using the ext drive and your Mac and try to take them somewhere that does Data Retrieval ... it might be costly but really, when it comes to our precious photos and files, the more backups you can do, the better ....
Over all, you have done some really good troubleshooting already, just fingers x-ed that the photos aren't lost ... and please promise to start backing up your data.