Assuming that the dns is in fact installed on the domain server then the dns points to itself;
1. Example, 192.168.0.2 Domain server with dns = point to 192.168.0.2* but internet options in the "control panel" points to the 1st proxy server address which I'll say is called proxy1 and resides at 192.168.0.3 just for example.
* You could of course also point it to the local loop address of 127.0.0.1 if for some reason you didn't want anyone but the domain to be able to reach any address outside of the domain… presumably there would not be any dhcp in this case or there could be conflicts.
2. 192.168.0.3 address of 1st proxy server and this could | should have a dhcp entry in whatever location runs the primary dhcp… ie, proxy1 = 198.168.0.3 so if we have this entry then we can just say "proxy1" and the system will (in theory) find its way out.
Imo both dhcp and especially proxy servers are old protocols which are showing their age now days.
I have to ask… Why on earth would you want 3 proxy servers… I assume they are not trying to connect them in series but as separate exit ports or you will have a routing nightmare.
Are you sure they are proxy servers and not just routers or firewalls?