First of all, I assume you both have this Mac:
https://everymac.com/systems/apple/...l-graphics-mid-2014-retina-display-specs.html
Secondly, no backups is not good. It is important to backup your machine (and your wife's also) to an external drive.
Third, here are some recommendations for software you can use for disk cleanup/maintenance/repairs:
Onyx - Available from here:
https://www.titanium-software.fr/en/onyx.html
Rock Solid, has been around a long, long time, and has had many positive reviews. I use it religiously (along with a commercial program entitled Tech Tool Pro). I would not be without either of them. In fact, I will not upgrade to a new Mac OS until there are compatible versions of both of them for the new OS (along with 4 other critical programs that I have). Note that there are different versions of Onyx available, for each different Mac OS. You would need to get the correct version for the Mac OS you are using.
AppCleaner - Available from here:
https://freemacsoft.net/appcleaner/
Another stellar performer! As you can see via that link, it will get rid of most stuff associated with an application that you wish to delete. Like Onyx, note that there are different versions for different versions of the Mac OS. You would need to get the correct version for the Mac OS you are using.
GrandPerspective - Available from here:
http://grandperspectiv.sourceforge.net/
Nifty graphical way to see which files are on your drive. Good way to identify large ones that you might not need.
Malwarebytes - Available from here:
https://www.malwarebytes.com/mac/
Good to use if you see adware and/or suspect you might have a virus. It also is good to run it every so often, even if nothing is wrong.
ClamXAv - Available from here:
https://www.clamxav.com/
More extensive than Malwarebytes in terms of finding viruses. You can use it in demo mode, and it still has just about full functionality.
Then, you should consider using either SuperDuper! or Carbon Copy Cloner to make a bootable backup:
SuperDuper! -
https://www.shirt-pocket.com/SuperDuper/SuperDuperDescription.html
Carbon Copy Cloner -
https://bombich.com/
You can use either them in "demo/trial" mode, although I believe you can use SuperDuper! in trial mode for more than 30 days. Using either of them makes recovery much, much easier. And you will have way more control over the process.
For commercial products, I use Tech Tool Pro (along with Onyx) on a weekly basis to keep both of my Macs "lean, mean, and clean". While Disk Utility is fine, it is not as extensive as Tech Tool Pro.
But for now, it is important to get your machine back up to speed. As long as you need NOTHING on your Mac, here is what you can do:
1. You need to purchase a Thunderbolt-to-Thunderbolt cable:
https://www.bhphotovideo.com/c/prod...t8aE3gIVCoZ-Ch1SdwMaEAQYAyABEgJfqvD_BwE&smp=y
2. With both machines turned off, connect the two Mac using that cable.
3. Boot up your wife's machine.
4. After your wife's machine finishes booting up, start up your Mac, but hold down the T key. Your are booting your Mac in Target Disk Mode, which basically means your internal hard drive will appear on the desktop of your wife's Mac, and it can be "operated" on:
Target Disk Mode -
https://www.makeuseof.com/tag/target-disk-mode-guide/
5. Launch Disk Utility on your wife's Mac, and let it Erase and Format the internal drive on your machine. This will erase EVERYTHING on that drive.
6. User this link to "obtain" the installation file for High Sierra:
https://itunes.apple.com/us/app/macos-high-sierra/id1246284741?mt=12
7. Click on Open, and a screen will appear to start the installation of High Sierra. After you click on Continue, and after you agree to the installation agreement, click on Show All Disks. Select the one for the internal drive on your Mac, and proceed with the installation.
Given that you have no backup, you then have a choice: either go through a new setup procedure (you'll need to establish an account, configure Network/WiFi settings, etc., or you'll the offered the opportunity to "migrate"/copy needed "stuff" from another computer. As long as your wife's machine uses the same Mac OS (and you and her have no "secrets"!), you can get most of that "stuff" (applications, setups, etc.) from her machine. But I have never done that, as I make two backups for each of my Macs each week.