Well, there's no easy way out of this. I'd go out on a limb here and say that you are dealing with someone with a load of insecurity. You're mention of her trauma history reinforces this.
Insecurities take a lot of time and work to get through. And there's not a lot you can do to speed the process. About all you can do is try to get her to acknowledge this and make her own commitment to work hard on it. It's after all in her OWN best interest - nobody else's.
In the meantime you might mention that it's really quite impractical for multiple people to be so intimately involved in each other's lives that everyone is witness to and takes part in everything each other does. Think about that ! Get some perspective.
She needs to realize life is going to go on for each of your unique little bubbles. Places you will go, conversations you'll have, feelings you'll experience, good solid craps you'll take
Everyone doesn't need to, nor should want to, be witness to it all
That of course will leave the sexual aspect.
That's it's own beast.
You'll either have to work towards building comfort being sexual in any pair or all agree to only have sex as 3sums. I think it will be apparent how unpractical that sounds too once you talk about it.
Reinforce that "ENVY" is normal but controllable. Sometimes people get/experience something someone else doesn't. And sometimes that swings our way. It's just how life flows.
Grin & bear it and be happy for the "other".