Eric, which version of Lightroom are you using and which OS??
Are the files showing where you asked Lightroom to import them to in Finder????
Can you post here some screen shots to show what you are seeing at the different stages please??
Finally I have time to answer you Geoff. I am using a Mac with latest sierra os 10.12.5 and Lightroom CC 2015.8. Here is the import screen. You can see the ticked images on the right hand panel, these are the ones I want to import. I press the import button but nothing happens. I leave the computer for 10 minutes but no activity is noted. I press the cancel button but again no action. I have to manually shut lightroom down and reopen in library mode. I can see, and access the images from the first sd card, but there is no record of the second images. I hope this helps you. Eric.
It could be there is a problem with the second SD card. Can you copy the photos from the second SD card to one of your hard disks using your operating system?
I see the cards are being recognised as Hard Drives as well as Devices.... is this with both cards??
There is an answer for this, let me ask around as I can't recall instantly!!
Do update to the current version as a first step please.