Hi,
For your questions:
As you mentioned above, sysvol not not syncing will cause the group policy issue .And the sysvol sync may caused by the ad replication or other issues.
So before any more changes in the domain, it is suggested to fix the issue firstly.
You can confirm if there are any ad replication problems or DC issues on each DC by command :
Dcdiag /v >c:\dcdiag1.log
Repadmin /showrepl >C:\repl.txt
repadmin /showrepl * /csv (It will report the replication situation for all the DCs)
If there are no issues for the ad replication ,you can try to fix the sysvol sync:
For FRS : you may try to do "D2"on the 2012 DC.(Before this,remember to backup the sysvol folder for the 2016DC and 2012DC.) https://learn.microsoft.com/en-US/troubleshoot/windows-server/networking/use-burflags-to-reinitialize-frs
For DFSR: You can try the non-authoritative synchronization on 2012 DC.((Before this, remember to backup the sysvol folder for the 2016DC and 2012DC.))
https://support.microsoft.com/en-us/help/2218556/how-to-force-an-authoritative-and-non-authoritative-synchronization-fo
Best Regards,