Using two Computers

I have been using a desktop for my work on my website. However, I find myself traveling a bit lately. Is it possible to use a laptop as well as a desktop for uploading from lightroom to Publisher?

yes, but what you publish from Lightroom Publisher will be catalog specific.
That is, you can only control albums made by a catalog with that catalog.
So if the catalog on your laptop is different from the desktop, you won’t be able to use your desktop catalog to control albums published from the laptop.
And you will not be able to use the laptop to publish to albums created on your desktop.

If you’re not using Lightroom Publisher (you’re uploading using Backlight Publisher) then you can use either computer.

Thanks Rod, So, can I use Backlight publisher on my laptop and lightroom on my desktop? Or is it difficult to just transfer to Backlight Publisher?

you can.
But any photo or album you publish with Backlight Publisher won’t be manageable from Lightroom

I’ve been a traveler in the past and found information available at https://www.lightroomqueen.com/ to be helpful in learning what files are needed to keep things in sync. I travel with a 4 TB drive that contains my photographs. I copy the information needed from my C: drive to that 4 TB drive them move it to the C: drive on the laptop. I’ve never Published on the road, just collected captures for the future memories. I reverse the process when I get home. I hope this is helpful.