From the way your question is worded, it seems your expectation is that when Windows needs to resolve a name, it will ask the primary DNS server. And if the primary DNS server doesn't know the answer, it will then ask the secondary.
I hope the above isn't what you were expecting, but if it is, then let me show you why that's a mistake.
DNS doesn't work that way. The only time a resolver will failover to the secondary DNS server is when the primary does not respond at all. An example will clarify:
Suppose you have a primary DNS server at 1.1.1.1 and a secondary at 2.2.2.2. Your client is configured with them in this order. 2.2.2.2 hosts a a private zone foocompany.local; 1.1.1.1 hosts no zones of its own, and does root lookups for internet hosts.
If your client tries to lookup someserver.foocompany.local, 1.1.1.1 will return NXDOMAIN (eg "I queried the root servers and they say that domain does not exist"). Your resolver will not then ask 2.2.2.2 what it knows, unless 1.1.1.1 fails to reply within the timeout period (usually 2 seconds). It'll just quit looking. Further, your client will cache the NXDOMAIN result, as per RFC2308. Even if you change NIC settings such that 2.2.2.2 is the primary server, you'll still get NXDOMAIN results until that local NXDOMAIN cache is expired. You can verify this by issuing ipconfig /displaydns at the command prompt.
IIRC, Windows' DNS resolver caches NXDOMAIN for a short time - 5 minutes. But still this can be annoying.
Anyhow. I realize this is a little bit tangential to your problem, but clarifying this point may bring about an epiphany for your planned design. EG: you may want the VPN's DNS server first to resolve after all. Although it is a tad slower, it knows more, since it can resolve both the domains private to the VPN and public internet domains; whereas the local LAN DNS resolver knows nothing of those domains private to the VPN.
Cheers!
Best Answer
You can prioritize one adapter over another. Read through this article for how to do it.
However, when you say "I'd like the DNS lookup to first try the default DNS for the LAN and then if there was no match, try the default DNS for the wireless.", that is not going to work. Your LAN DNS Server, if available, will either resolve the name for you, answer that the name does not exist, or refer you to another DNS server. While you might think that the third option would be your ticket, understand that the DNS resolver in Windows (an most other systems) is a stub resolver that can not follow referrals, and so your DNS query will fail at that point.
If what you truly want is to get the internal IP adresses of your systems when you are connected through your LAN, and external resolved addresses when connected outside, or in general for any external names. This can be achieved by setting up split DNS on your LAN DNS server.