You have not given enough information, but I will try to give some pointers in the right direction.
I have seen similar authentication problems on complex NT domain structures. Commands will be executed without any errors, but without making thechanges that the commands were supposed to make.
Are you running separate NT domains, or a 2000 active directory?
If you are running active directory, are the 2 domains in the same tree? If you are using NT domains, are there trusts in place between the 2 domains?
If there are no trusts in place (NT domains), or the domains aren't in the same tree (active directory) then this could be the problem. The SID for the 2 users that have been created in the different domains is different. These 2 users will be considered to be different users because the SIDS differ. The account from Domain_2 will not have permissions on Domain_1 to change anything that requires admin privileges.
A better way to do this would be to use the account from Domain_1 in the runas command to change the time on the server server_1. You can still get the time from an un-trusted domain.
I hope that this makes some sense! It doesn't seem to when I read over it!
Regards.
Duwane