I can't help but say that I can't imagine thinking of someone as "family" until I'd had a good long while -- at least a year, I think -- of knowing them and relating to them in person. The troubles you all have run into seem like they could have been mitigated if you all had had more time to feel out the dynamics between you before moving right into co-habitation and family mode.
That said, her coping strategy would be really problematic in any relationship. Is she open at all to the idea of therapy? Can she explain why she does this with you and not your other partners? I know you said that you thought it would the healthiest for you to not even be friends with her, but maybe she wouldn't feel the need to be so emotionally careful if you and she were just friends?
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.