Please explain more about your problem. You have said "I can't access with single signon". How are your child sites configured (give examples of the URLs of their home pages)?
We have several sites running in the mode you are describing, using hostnames for the different sites (e.g. our sites are a.site.com and b.site.com) and single sign-on works fine. However, do not expect that signing in on one site will automatically sign you in on the others - you have to sign in on the other sites as well, but you can use the same credentials. So "related site mode" means the same user accounts work across all the sites, but you still need to log in on each one.
We have never actually tried it, but I think if you were running child sites based on folder names, with related sites mode, then you would only have to log in once for all sites, as the authentication cookie would be shared by all sites. I could be wrong here!