Depends on your age- if you're underage. Your parents have a right to generally know what's going on in the sessions. I believe even among Ts there's a disagreement how much and what they need to share but reporting the SUI thoughts/plans is stg the majority (if not all) Ts agree upon.
BTW I don't think checking your mum's personal mails is OK- saying that it's her 'fault' cause she knows you know her pass is just a rationalization. I too know my mum's (and sis's/dad's and they know mine) pass and check their mails ONLY if asked. It's based on mutual trust.