The wiki does explain this but its a bit convaluted, who ever rights Sam's needs to clean it up a bit(maybe seperate it into Slave/Girlfriend routes the way Bree's is seperated between gamer and maid, but I digress, what your looking for should be at the or neer the bottom of "path A"(don't ask why i have no idea) but it should start around "Samantha wants the truth" and you can't lie or say she's the only one witch means her KP NEEDS to be at least 75, so i don't think you need to collar her(doesn't hurt though lol) once her KP is max'd and she's asked you to tell her the truth about wether or not she's the only one you should be able to talk to Bree/Sasha/Minami/Lexi(if Lexi is already a member), go to the "chat" screen when girls are home and you should see a Samantha icon, I got a forced event to talk to them when both Bree and Sasha where at the pool(home) where it just sort of forced the topic(same thing with Minami joining actually) after talking to the other girls and "chating" about Samantha you have to call Sam at a specific window of days/hours(any day but between 9-18 i think) and it should force MC to ask Sam to come over, just make sure both Bree and Sasha's KP is high enough.