I have never had any luck depending on XMP sidecar files to preserve edits from one LR installation to another. I have read about using them as a failsafe in case of a catalog crash, etc, but every time I have tested this, it didn't work (if anyone knows differently, I'd love to have it explained - I have seen several blogs touting this, but it has never worked).
What we do to share edits between systems that has worked reliably for years is "Export Folder as a Catalog" (we keep the photos in a "job" folder so they are easy to export like this) from one computer and then Import the Job Catalog into the 2nd computer. All edits, edit history, settings, etc come over fully and can be worked easily by another editor or the same editor on a different system (but only one system at a time - if you need to go back to the original computer, you have to do the same Export/Import process again). Try that to see if it works for you. You don't need to create new catalogs or switch catalogs or anything like that; the imported catalog simply becomes part of the existing catalog.
Note: if the images are already in the location you are exporting to and you only want to update the catalog with edits (for example, moving your on the road edits back to the main computer), then you can uncheck the boxes for exporting negative files and probably previews as well.
Recently, I edited a wedding on the desktop and then exported the XMP data so I could view and continue editing it in Lightroom on my laptop while I was out of town. The color is SO off when I open the photo in Lightroom on my laptop!
There's a lot of information missing from this statement.
You can't really export XMP data, you can write the XMP to the photo file (or in the case of RAW, to the sidecar XMP file). Exactly, using Lightroom words, please state what you did.
When you "open the photo in Lightroom on my laptop" ... exactly what did you do? Is this an import? Or did you somehow transfer the XMP but not import? Exactly, using Lightroom words, please state what you did.
BOTH COMPUTERS ARE CALIBRATED (just want to make sure you read that part!).
I read it, but I'm not sure what you mean. Do you mean that the monitors are calibrated? OR somethine else?
Lastly, to use a very literal interpretation of the words in your title ... the appearance of photos in Lightroom do not have to match if the XMP files are identical. Why? Beause Lightroom, by default, does not use the XMP files to render the appearance of your photo. It uses the information about the photo in its own database, which can be different even if the XMP files are identical. If you want Lightroom to use the information in the XMP files to render the appearance of the photo, you must specifically instruct Lightroom to do so, manually, via the command Metadata->Read Metadata from Files.