Hopefully you have created a folder structure that puts everything within one master folder. You can have numberless subfolders, but it's really best to have everything within one master folder. If that is how you have the images organized then simply copy the master folder of images and the catalog to the external hard drive to give your ex-wife. If the drive containing the images has a different designation on her computer, all she has to do is update the folder location of the master folder and go to work. On your computer, I would suggest using Finder to copy all of the images to the external hard drive. That means the images will be in two locations. After you have copied the images to the external hard drive, just start Lightroom and update the folder location of the master folder pointing Lightroom to the folder on the external hard drive. Once you have done that you can remove the images from the Mac hard drive. One thing to be aware of is that your ex-wife will have to be using Lightroom 6 or Lightroom CC in order to use the catalog. If she is using an older version (i.e. Lightroom 5) she will not be able to open the catalog.
Please read the section "Part 2 — Updating Folder Location" of this document for detailed instructions on how to Move photos to a new location. Adobe Lightroom - Find moved or missing files and folders