OK, I think the word 'persistent' led us in the wrong direction :-)
Yes, an installed system is portable between computers
An installed Ubuntu system is portable between computers, but not as portable as a live or persistent live system. If a computer needs a proprietary driver for example for graphics or wifi, there is a problem. You should avoid proprietary drivers unless all the computers would work with that/those particular driver(s).
Edit: You can install Ubuntu into a USB pendrive like it were into an internal drive, and it will work also in other computers. Install it from the live system in one USB pendrive into another USB pendrive (and avoid proprietary drivers).
Particularly If the computer is running in UEFI mode, it will be much easier if you unplug the internal drive before you start installing. Otherwise the EFI partition in the internal drive will 'hijack' the bootloader and you have to fix a bootloader in the USB drive manually afterwards.
After the installation you can re-connect the internal drive again, and it should be possible to use a hotkey to get a temporary boot menu, where you can select the USB drive (or the internal drive). Without that hotkey, the computer should boot directly into the internal drive (and your wife's operating system).
If the original drive and the target drive have the same size sectors, you can clone the system (from a smaller drive to a bigger drive) for example with Clonezilla.
Otherwise you must extract the files, fix some configuration files and create the bootloader separately. It is possible, but I think it is faster and easier to create a new installed system (or persistent live system) in the USB drive, install your favourite program packages, configure the system and copy the personal files that you want.
You can create a script with rsync or use Unison to syncronize the personal data files between the two systems.
See these links
Try Ubuntu (Kubuntu, Lubuntu, Xubuntu, ...) before installing it
help.ubuntu.com/community/Installation/UEFI-and-BIOS
I would like to make a usb bootable that boots up to be the same as what boots up on my hard drive now, with all the extras I've put in it.
I should be able to walk up to any PC, plug in the usb and boot to my familiar machine.
Do able?
– LarryM Mar 27 '17 at 02:37