What should I do? Which technique to use?

[MrBond]

First off you don't have to apologize to her. You were only suspicious because she had actions that made you suspicious. She has no right to "test" you.

And come on. All she does is FB and asks YOU to make breakfast for her? Then threatens to leave you because you look at her computer? You're not her butler. SHE has to earn your trust. Not the other way around.