Should be pretty simple. Haven't tried it myself yet, but a lot of people on Reddit mentioned already that they play it at their parents home, etc. so it can't be that difficult.
If you have everything set up already I guess the only thing you need to do is set up a "new home" in the Google Home App and then you should be able to start Stadia via that room. See the quick guide here.
Your games are anyway connected to your Stadia account and therefore your Google account, so you'll not lose any games if you change the WiFi connection.