Logon To Specific Site AD DC’s

I have one Active Directory domain and three sites. The problem I am having is that users from site #2 are loging on to domain controller #1 and #2 but the domain controller for their site is domain controller #3. I have installed DNS for DC #3 and created site links and a site subnet for the sites and have also made them all GC’s, but some of the workstations for site #3 still randomly logon to domain controllers #1 and #2.

Can anyone tell me how to make all of the workstation at site #3, only logon to domain controller #3, unless domain controller #3 fails, then logon to domain controller #1 or #2.