Lightroom sync allows you to sync files between your Computer and your mobile devices e.g Phone and Ipad. You cannot sync from computer to computer.
In addition you can only sync files from one Catalog at a time. If you proceed to sync a second Catalog you should get a warning that your previously synced files would be deleted from the Cloud storage and your mobile devices will loose connect with the previous Catalog images.
Also there have been some updates to Lightroom Mobile App and you can get some info from the link below. I find this site very informative in keeping one uptodate with Lightroom.
If you had copied your existing catalog and images to your new laptop then Lightroom should have allowed you to open that catalog and use it. The images that you had synchronized in that catalog should still have been synchronized.
Interesting Jim, have you tested this. I would have thought the system would recognize that there were two different computers?
You might be right. I have synchronized from my desktop, and looked at them on Lightroom for the web. But I don't have any mobile devices.
Jim is correct, just copy the catalog and images and backup files to your new hard drive. Open the catalogue via the menu commands. then it should load up. You will need to log out of your mobile account on your husbands computer then you can log in from your laptop.
now it might give you a warning about losing pictures but check your catalogs and see if they are all there. if they are then you just need to re sync photo's to the cloud.
if you have made changes to those files in the cloud make sure they are synced before you copy the catalog.
If, when you load the catalog you get "?" beside your photo folders, select the first folder in your library (possibly called Lightroom). right click and select "Find Missing Folder". Navigate to where your copied your library and select the folder you are looking for. once you selected that Lightroom will find all the folders inside and the "?'s" will disappear.