You cannot synchronize 2 Computers the way you are trying to. From your desktop computer you can create collections using Lightroom that can be shared and then you can work with those images on your mobile devices. Additionally, with your laptop you could go to adobe.Lightroom.com and have access to those collections. But you cannot access catalogs on other computers using the cloud. The catalog must be local to the computer that is running Lightroom.
I am just wondering how you would share a collection to my mobile device.
I travel with my laptop as my secondary computer to my desktop at home and would like to share images whilst i am away. Is there a way i could share a collection to my phone and share the images from there?
Please start your own thread on this topic.
You can share a collection from LR Classic CC to LR Web and to LT CC Mobile as has been pointed out from One Computer.
Whichever computer you want to do that from is up to you.