The last few times we've played, it's been pretty quick and simple.
I start Stadia and load game and click on Multiplayer. (I've been using the mouse while doing this instead of controller because it seems easier) I create the lobby and set to 2 players, Invitation Only. I Launch the lobby then load our Save Game. Now is when I usually connect the controller via USB cable to my PC. I invite the GF from the Session menu. She accepts the invite, and then pops into the game.
One time we did this we were not in the same "Party" so that we couldn't see each other on the map and presumably wouldn't have shared XP. This was easily remedied by simply going to the Main Menu and loading the same save game I had previously loaded. Then all was well.
*When I mentioned before about creating a new lobby, I mean that I create a lobby then she clicks on Multiplayer to see if she sees me. If she didn't, then we both go back to the main menu. I then go to Multiplayer and again create a lobby, and she clicks on Multiplayer to see if she sees me. However we haven't had to do this the last few times*