Just to clarify, the internet disconnect happens whenever I'm 1) within range of my wifi router and 2) activate my wifi connection on my phone (which automatically connects to the router's SSID). If the wifi connection function on the phone is already active when I come into range, it doesn't interrupt the internet connection.
And yes, my wireless router's SSID is broadcast, assuming that you mean that its name appears on an app such as WiFi Manager.
One other point of clarification: I've never used the hotspot function with the signal from my home wifi router. It's only been used while on the road and, as I said, not for some months.