If your family is loving and accepting, and you're at a place where you feel it's time or it's helpful to you
to tell them, and you could handle a worst case scenario, then tell them.
My family loves me very much and was not involved in my abuse (although they did unintentionally parentify me,
but that is because they didn't know any better having grown up in a bad home) so it was safe to tell them.
Before I lost my mom she was very supportive although she was very sad about how it came to be.
My dad doesn't like talking about any sort of things he considers not bright and happy. He accepts it just doesn't
know what to do with it. So I go to my "Second Family" for support.
My second family is the friends that I have made that support and understand who I am.
I know a lot of abuse tends to happen in the family of origin and that makes it unsafe a lot of the time to disclose.
In my case it didn't happen within in the family (rare maybe?) although what was happening at home made it seem impossible
to seek help from them so I was by myself fending off what was happening outside of the home.
Tell only the bare minimum. No one NEEDS to know you have DID. I found that bringing my friends to talk with the therapist
and watch United States of Tara together and have them ask questions about it (eg. does this happen to you) ...
However my friends already KNEW something was up... it just explained what was up, that's all.
Remember that some people do not believe in the diagnosis, some people will be uncomfortable and not want to hear it,
and others will try and manipulate your diagnosis (I had one person trying to call out my kids and manipulate them to do things behind my back, cut that guy out of my life once I found out) so be safe!

If there is a status quo in the family "everything has to be perfect" it will generally not be received well.
I've known someone who pointed out the problems in their family and then was LABELLED the problem! Although they
were they only normal one! Be good to yourself and take care.