Unfortunately, it's often one traumatic incident that will completely change a cat's behaviour. Having a claw stuck in Scully's eyelid did it for her, and it seems she has lost the confidence she once had, and is fearful, and with good reason. I agree that she isn't the happy cat that she once was, and likely a home where she's the only cat would restore her confidence. In the meantime, I would try and keep her in a separate room from the other two cats, or if there's one who will behave with her to keep her company from time to time. It doesn't help now that she runs in fear and has the dogs after her too. Because she wants "to be around everyone", you could have her in a large dog crate. That way she can observe, be part of the family and be safe from harassment.
"We humans are indeed fortunate if we happen to be chosen to be owned by a cat." -- Anonymous