Tricky situation.
Since Safari is an integral part of the OSX it can only be installed with the operating system, there is no separate install. Sounds like an underlying file has been corrupted or an install update did not complete.
You can boot in "Safe Mode" and test launching Safari. Safe mode disables any add-ons or extensions. If Safari works you will need to research steps to isolate issues in Safe Mode.
Start up your Mac in safe mode
- On your Mac, choose Apple menu > Shut Down. After your Mac shuts down, wait 10 seconds.
- Restart your Mac, then immediately press and hold the Shift key.
- Release the Shift key when you see the login window.
To get a browser you can go to https://www.mozilla.org from another computer with a working browser.
Download Firefox for Mac ( great browser )
Copy to a usb stick to transfer to your mother in-laws computer and install.
To the best of my knowledge the only way to do an install is to reboot in "recovery mode" and follow prompts to reinstall the operating system. Turn on your Mac and immediately press and hold these two keys: Command (⌘) and R. Release the keys when you see an Apple logo, spinning globe, or other startup screen.
NOTE: You will have an option to launch Safari, this is another test.
I hope this helps