Apple screen/file sharing issue
VNC style screen sharing is not really designed for use over the internet. The protocols are slow and require lots of bandwidth, plus dynamic ip allocation from ISPs can break it if you're not using a ddns service.

For this purpose you are much better of using some software other than the built in stuff. There are good commercial ones for $$, but also free options that do the job just as well.

I personally use NoMachine, which works across macOS, Windows, Linux and has mobile apps.

I have also previously used TeamViewer with good success.

For your use case, both of these options will be free, should be fairly reliable and will have more functionality than you probably need.