@PeteQuad No you can not. Your would have to have two accounts and two instances. I believe there are a few threads on Reddit with in depth explanations. Stadia will eventually come out with "family sharing" but that's not going to be a feature until some time next year.
@PeteQuad It really depends on what the game supports. If the game supports local co-op, then you definitely can play with friends/families under the same account.
I just tried it with Samurai Showdown, and it's allowing me to connect two controllers to fight against each other, under one (my) account. If there's any game that support 4 players, I'm assuming you can also connect 4 controllers to play that particular game. And you don't have to use Stadia controller. Here's a list of the supported controllers - Stadia-compatible controllers and screens
So you definitely don't need to have multiple accounts to play together, but it really depends on what the games.
Edit: I just saw that you're planning to use it in living room, which I assume you'll be using TV. As of now, you can only play on TV using Stadia controller, which fortunately you can buy separately. You can play with other controllers on computer.