email access credentials

I have been struggling to find a plugin that will allow me to keep my site private but send invitations by email that contain access credentials.
I am going travelling and want to allow my kids to see where I am and comment on posts that I make. Unfortunately my ex will not allow me to have there email addresses so any invitation will have to go via her.
I want to set up accounts for all family members so that they can just click on a link and they will have access and be assigned a username.

Does such a plugin exist?

I have searched and searched and the result has just been more confusion.

Any help would be very gratefully received.

Edward