How to load an existing, synced iTunes library on a different computer with a different library, without overwriting

I’d really like some advice on how best to undertake a recovery project.

I had been using iTunes on a Lenovo PC, which I had synched to my iPhone. The hard drive on that PC crashed. But I had all the files backed up on an external hard drive.

Fortunately, I have another, identical PC that had been my wife’s. It has iTunes installed, but had previously been used with her Apple Music account.

From reading online, it is always emphasized that iTunes should be fully updated before starting any complicated tasks. But to update iTunes, I need to log in, right? Should I log in as my wife, or as me? Is it not essential that I update iTunes before starting the work below? Or should I just delete iTunes from the computer entirely, and do a fresh install? Will it then ask me if I want to link to an existing library on my computer?

I had also read that if you hold the shift key while starting up iTunes, it will allow you to select which/whose library to boot up with. Is fixing my problem really that simple? But even if it is—I had read two different things—that my backed-up library just had to be on the C: drive, or that it needed to be saved in the Music/My Music folder. Or can I leave it right where it is, on the backup drive, and just point iTunes to it?

Prior to undertaking any of this, should I turn off “Synch Library” on my phone, leave it on, or doesn’t it matter?

And do I need to delete any of my wife’s music files before I start any of this?

My main concern is that even though it’s my existing library, it’s on a different computer. If it’s not recognized as my existing, same-old library as was previously synched with my phone, will it wipe everything off my phone and replace it with what is on my computer? Vice versa? The two libraries should be very similar, with the only difference being the music I downloaded or deleted on my phone since my hard drive crashed. But deleting then replacing my whole library on either device, were that to automatically happen via a synch, would use a ton of data and take a ton of time.

In closing (sorry for all the questions!), my take is that *possibly* this isn’t really a big deal at all. I’m just trying to be extra safe and avoid any catastrophic errors. I get that I’m lucky I had a backup, and my current issue is a (comparatively) good one to have.

So, if you could give me advice on how to get back to my prior situation (iTunes with my backed-up library working like a charm on my backup/wife’s PC, and that successfully synched with my iPhone), I’d be endlessly grateful. Let me know if there’s any very important sequence in which to do the steps, and/or any potential pitfalls along the way. Thanks in advance so much!