Ok so the forwarders tab also has those same DNS servers in?
Site A is using 192.168.0.101 is that a Windows Server?
How is DHCP assigned to Site B is this a Router/switch?
Can you do the following:
> on the DNS server create a new reverse lookup zone for 192.168.1.x
> on a client in Site B configure a manual IP address (in the correct range) enter the following, subnet=255.255.255.0, gateway=192.168.1.1 and enter a single DNS address as 192.168.0.101
> on the client in Site B run IPCONFIG /REGISTERDNS then IPCONFIG /FLUSHDNS
> check the DNS forward and reverse zones to see if the client has registered?
Don't worry this is purely for testing I am not going to ask you to do this for all clients I just want to make sure that what u am suggesting to you will work.