I would use the home WiFi initially, the hotspot on the Pi4 can be a bit weak at times.
To get it all working and ensure good connectivity in the first instance use a network cable if you have one direct to the modem router, then switch to the home WiFi once you have it working as it should. Take it a step at a time and you shouldn’t have any great issues

From my experiments with the hotspot on the Pi4 it appears to work best when there’s no other WiFi signals about for example in the middle of a field.

Regards Alan