>>> would PC download work on her tablet?
Not a chance. (Sorry!) Windows and Android (which Amazon Fire OS is derived from) are totally different operating systems. Windows software has to installed to the computer's 'registry', whereas Android doesn't have a registry at all.
Amazon offer their Fire tablets so cheaply because they then force you to use only their own download site for apps. That, in turn, limits what's available to users. It is possible to add the Google Play Store to an Fire tablet, although it's a bit of a fiddly process:
https://www.howtogeek.com/232726/how-to-install-the-google-play-store-on-your-amazon-fire-tablet/
Once you've got the Google Play Store onto your tablet you can then download a far wider range of apps, including The Sims Mobile:
https://play.google.com/store/apps/details?id=com.ea.gp.simsmobile&hl=en
However The Sims 4: Island Living isn't available for Android devices.