To think she should be past this now?

Cousin babysits for me a couple times. A few months back I thought I had been burgled. I asked my cousin if they locked the doors when they left the house and also if they had heard about what had happened to the laptop (it got broken). I was not accusing them. Just asking and I made this clear.
They said they felt uncomfortable having a key and also upset about what I had said. I apologised deeply but they still said they did not want a key. This week I go on vacation and asked cousin if they would keep the key. They said no and said they didn't feel comfortable still. What else am I meant to do to prove she is trusted?