It all started simply enough. While wandering out in the wilds, I encountered a dwarven prisoner who shot at me once and then started screaming for help. Nearby was an elven recruit, so I killed that one and then chased the sprinting dwarf. After some cajoling and small talk she was inclined to join me (I think the first time I tried, she immediately broke the agreement and resumed attacking me). I picked up the crossbow I'd taken off her, and gave it back. Job done, apparently.
Some time later I remembered I had a spare shield in my inventory, and gave her that. Upon checking to see whether she'd got both the crossbow and shield equipped, I noticed that both were crammed into her quiver. My previous experience with trying to swap companion equipment through trade was that it is a pain in the bum, so I cancelled her travelling agreement and then strangled her. In retrospect, I probably just could have taken the quiver while she was conscious.
Naturally this escalated the conflict right into No Quarter, but after enough non-lethal damage and a request to stop fighting, she did. During the combat, I also asked her about herself and talked about the weather. Dunno if that helped any. Then I asked her to join me, and she accepted and didn't attack me. I gave her the crossbow and the shield from out of the quiver, and she held them properly. Then I gave her the quiver with the bolts still in it, and she wore that. Unfortunately, I haven't yet found anything to attack, to see if she'll shoot instead of running in with fists or crossbow.