So I setup a VPN connection to our remote office where the child domain server is running and was able to get past the first error. Looks like you are correct in that the Sync machine needs to talk to all the Domain Controller.
The next error is"Log on error: unknown user name or bad password"
I double check to make sure both accounts (o365 and local domain admin) are valid. Run it twice and still have the same error.
I remember reading this thread: community.office365.com/.../161884.aspx, where someone also has 2 domains and it looks like DirSync is trying to logon to the child domain controller using "childdomain\administrator" with the same password for the primary domain.
Can you verify if this is the issue? That the sync program is trying to log in in all domain controller using the same account that we supplied in the second screen?
Thanks for your help,