How to get access to hidden folders from another Macintosh HD (Users/Applications)?
Since your failed system was on Catalina, which uses the Read-Only System Volume scheme with separate System and Data volumes, it sounds like you backed up only the System volume. The /Users directory, however, is stored in Data.
One possibility for why you did this is that the Data volume might be corrupted and unmountable and therefore didn’t show up in Disk Drill, so the System volume was your only obvious choice.
Another possibility is that High Sierra is two major OS releases behind Catalina. In general, it is inadvisable to mount an APFS volume from one OS using an older OS because APFS is a moving target and there are changes and additions to the format &amp; filesystem driver that occur between releases. While unlikely, your wife’s machine may not be able to recognize the /Data volume. (It’s also unlikely but possible that mounting it on the old OS could have unintentionally caused damage to the newer format.) I haven’t used Disk Drill so it is possible that it did image your entire drive and the Data volume is still hiding in the .dmg, waiting to be read on a newer OS.
As a general rule, any time disk corruption is suspected, your #1 goal is to minimize disk usage (especially when hosted on the faulty machine) until you’re ready to perform a repair or transfer. Repair is no longer an option since Disk Utility couldn’t do it and no other APFS tools are currently available. So you’re left with transfer.
To maximize your chance of transfer, you need to be running at least the same version of OS on the lifeboat unit. You would also ideally be able to remove the physical drive from the target machine and place it in an external enclosure. Even so, your chance of success is slim if the Data drive failed to appear. You do need to be able to accept the fact that your data may be gone. (You could take out the SSD and set it aside, waiting for DiskWarrior 6 to come out and give you another chance at recovery.)
In short, try again with a Catalina machine, but minimize how much time the drive is powered on and be ready to call it a day.