You ask such interesting questions. I keep having thoughts 
You ask about shame in not doing what you said you will do. Obviously you want to be sober - you wouldn’t be asking here if you didn’t - but there’s a doubt in you.
The question you’re asking here is about the core sober living question:
accountability
Ultimately being sober is about choosing to be sober every day, for that day. It involves making the choices you need to make, to be sober that day.
You do have to be accountable to people. People do need to know that you are sober, and walking your sober path.
In my experience family members have a lot of emotional intensity associated with them. That’s not good or bad, it just is what it is.
In addition, family members are also often not trained in recovery. Recovery is a multifaceted emotional and social experience, and it is not for people who aren’t willing to put in the effort. It also requires a lot of reflection and soul-searching, and support from people who have walked the journey. (It is difficult for people who haven’t been through recovery to fully understand the process.) This is why AA or another similar recovery group, works. It is an organization available free of charge and populated by millions of people who have walked a recovery path, and can coach you along yours.
You do not have to tell your family. But - you do have to be accountable to someone, and you do need someone you can call. The benefit of choosing a recovery group is that they have the expertise and the experience, to help you walk your path.
There’s a good selection of groups here: