Just to get us all on the same page, this is no longer a "can't-see-on-the-network" problem, and all three machines connect to the internet fine. ("Office" connects to the internet by ethernet, and "Kitchen" and "Unit" connect via Aiport on the router that Office runs through.)
This is a problem of local networks' "Name/PW". Office (mini 4,1) can connect to Kitchen (mini 6,1), but not Unit (MBPro 8,2). These two can't connect with any machines.
The confusing part is that the only possible connection (Office->Kitchen) is made by entering Kitchen's current user account name and PW on Office (when requesting access). I would have thought that the requestor would have to give his own name/PW, not the name/PW of the machine access was being requested to.
When it comes to the other two machines which can't connect with any machine on this network, it doesn't work whether the name/PW I supply is the requestor machine or the requestee machine. The network refuses all names/PWs.
This isn't a matter of getting names/PWs wrong. The names come from SysPrefs>Users&Groups>CurrentUser. All current user accounts are Admin. All three machines are running on the same OS 10.11.6.
I'd like to solve this problem, as the frequent fall-back on thumb drives is getting old.
Thanks in Advance to All,