If you store your edits on xmp and reimport the images in Lightroom, then Lightroom will be able to read the edits but it would not be able to list the changes done in the History Panel.
Each and every proper step is not recorded in the xmp file, only Lightroom Catalog keeps track of the history steps.
You can either copy the complete catalog from your laptop and paste it onto your desktop
Or, select the images in your Lightroom Catalog on your laptop and go to File> Export as Catalog
then, move that exported catalog onto your desktop and relocate the missing images with the new location on your desktop.
You can also refer this article : http://tv.adobe.com/watch/the-complete-picture-with-julieanne-kost/how-to-migrate-lr-to-an other-computer/
Thank you for your email. I can't understand why all the steps are not listed in the history. Is this something that will be addressed in future updates? What is the point of xmp files otherwise?
The problem now is that I've "removed" the pictures from the catalogue on the laptop. So I can't export as catalogue like you suggest (even when I re-import them on the laptop, the history steps are not listed). Have I lost the details of my edits for ever?
It is the property of xmp file that it stored the edits and metadata but does not the keep a track of proper history steps performed.
If you removed the images from your catalog on laptop, then I'm afraid there is no way to recover the history steps until you had a backup of your Lightroom Catalog on Laptop which you can get hold of.
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I can't understand why all the steps are not listed in the history. Is this something that will be addressed in future updates? What is the point of xmp files otherwise?
This is as designed and I doubt it will be changed. The xmp data only records the final settings of the sliders, etc for the photo. For instance, if you have a +5 final contrast it is unimportant to the final photo that you moved the contrast slider a dozen times to get to that point. If you want to keep your history, you can use export catalog from the laptop and import catalog to the desktop to do that so why would Adobe need to duplicate this in the xmp.