If Renee is a baker who gets up at 4 AM and Brun is a bartender, who will traditionally get off work at 4 AM (probably later) when do they hang out? Do they have any overlapping awake-and-not-working hours? Are their friendships based exclusively on brunch on their mutual days off and phone tag? Sure, Brun seems to have had an earlier shift at least when she met Clinton, but if that is her regular shift, that is even worse. She would be starting work when Renee gets off work. Plus, the chances that they have the same days off regularly are pretty low - both those jobs often have regularly changing shifts, in my experience.
Maybe that's why Renee is so possessive. She never sees her good friend anymore, and is feeling really insecure about their relationship, and her friend just went through a massively traumatic event, which is something Brun can't handle very well, and as jheartney pointed out, Renee probably is aware of. Awww, she is just insecure and worried and trying to be a good friend and overcompensating.