I think I would "pay" him to take her out more :-)

Since she's acting like a child and your son still lives with you; I'd set ground rules on arguing; if either/both argue too long/loud/annoyingly, then they have to leave, go somewhere else because "no one else wants to hear that". It's not an attack of their person, just their style of behavior and just as you'd expect your son(s) to behave in your house, you expect your sons' friends to behave!