I'm trying to install our licence on a laptop and a desktop. The desktop is installed, but the serial number is reported invalid on the laptop - the licence is for both right? The desktop is Mac and the laptop PC - is this the problem?
Yes, this is a problem. In general, a license is only applicable to one type of operating system since different software is created for different systems. So either both machines need to be PC or both need to be Mac.
The only exception, which drives my use of the words "In general", that I know of involves Photoshop Elements which can be used on multiple platforms. All other licenses are only good for one OS type.
You are better off contacting someone at Adobe directly if you want to see if there are any exceptions pertinent to your situation, though yours is a fairly common one, so chances are the answer will be that you need to buy a new license.
Which Adobe product exactly?
Photoshop Elements, Premiere Elements and Lightroom are all multi-platform serial numbers - work on both Mac and Windows.
Serial numbers for all other products are operating system specific.
(Note: Adobe Creative Cloud products are all multi-platform too but they don't require a serial number. Adobe ID only.)