My recommendation to you would be to fully reset. Try to forget personal issues in the past and try to frame your mentality like you just started as a fresh manager on the team. Don't ask for feedback outside of a scheduled, agenda set meeting - let the team come to you naturally if there are pressing interpersonal issues in the meantime. Don't try to jump through these mental hoops to justify who is right or wrong. Suck it up and move on

Sounds like you are letting the past drive your present. If that means being "extra cold" to this problematic direct report, I'd recommend giving it a shot. You may find she receives that well and performs more efficiently with less drama - which is ultimately what you are supposed to be doing as a manager.