DNS settings on managed switches in LAN

Solution 1:

You want to specify the IP address of the name server you want to use. That sounds cyclic, perhaps, but that's what you want.

Some Sonicwall appliances have an option to run a DNS server. You're almost certainly running a DNS server on this Windows Server 2008 if it's acting as an Active Directory Domain Controller. The Windows Server 2008 machine would have a richer configuration interface than the Sonicwall, so I'd opt to use it as the DNS server for all non-Windows devices on the network too.

The DNS server specified on switches typically only controls how the switch itself resolves names. It will have nothing to do with how devices attached to the switch resolve names. Don't get wrapped up in thinking that the DNS server specified in a switch at all alters how clients interact with DNS. (This is true of most embedded devices, excepting consumer wifi routers, which typically offer up their own mini DHCP servers and may either offer DNS services or automatically direct clients to the upstream DNS server.)