Vash eventually finds out that Wolfwood is married to the arts teacher Milly. What makes it worse, she is the sweetest person he's met in a while and they look so cute and loving together.
Vash befriends a woman, by the name of Meryl, who he assumed is another mother. But whenever he sees her, she never picks up a kid, just talks to the teachers.
So he asks her who her kid is and she goes "Oh I'm not a parent, I'm just here to pick up my girlfriend" and then Milly walks up to her and kisses her like "Sorry, just 5 more mins I have a few more things to do."
And that's how Vash finds out they're in a closed polyamorous relationship.
He wants to ask more questions but is afraid that he'd be invasive. But one day Meryl has had enough of it and just tells him to spit it out and ask what he has to ask.
After a long discussion with all three of them, he asks if he could "join them". They talk it through and agree to give it a shot.