I would suggest you to create a catalog on your laptop when you are not able to access the desktop computer.
Once you are back, follow the links to transfer the catalog and images on the desktop computer.
Once you have it transferred, please follow the steps provided in the below link to merge the catalog and create a master catalog.
Let me know if this helps.
The Lightroom workflow is controlled by a "catalog" file, which is a database. This catalog keeps track of the location of your images as well as all the adjustments you make in the images. The Lightroom adjustments are not applied directly to the image file. Your images are always in the same state they were when they were imported from the camera. The catalog must reside on a drive that is local to the computer using Lightroom. The catalog cannot be stored on a network drive. However, the images can be stored on the network drive.
In a workflow such as yours, the best option would be to keep the catalog and images for the Mac laptop on an external hard drive. You can make all adjustments to the images. Then when you get home, you can plug that external hard drive into your desktop PC and import from the external hard drive. That will transfer the images as well as all the adjustments you have made to your PC at home. If an external drive is not practical then you could create the catalog and store your images on the hard drive of the Mac. Then, when you get home, you could export the catalog and images to your NAS drive and then import them into your other Lightroom catalog.
The creative cloud provides a means for you to import images to either your desktop PC or your Mac laptop and then create what is called a collection. This collection can be any type of grouping of your choice, i.e. a certain destination, a certain family, a wedding, etc. Then that collection can be synchronized with Lightroom Mobile, and it is possible to make changes on a mobile device. Any adjustments made on the mobile device will be applied to the images on the computer where they are stored.
I don't know if any of this has helped. But feel free to ask more questions. Perhaps there are others who will have better insight than I have.