Thanks for all the input guys--cmetz especially. Sorry for the late response, but I've been away for a few days.
sieist, merc: What I was trying to do was pretty much a vlan without any specialized hardware.
Haha, now I am going to describe what my situation was. Let me say again, I do know what I am doing, and I definitely realize that this is not the best (or even a good) way to go about this. This post was more of an academical inquiry than a request for comments.
Internet connection #1
--------------------------
Cable modem with integrated NAT router (and 4 port switch) handing out 10.1.10.x
Internet connection #2
--------------------------
DSL modem -> Netgear wireless NAT router (and 4 port switch) handing out 192.168.1.x
Sooo, I had a necessarily wireless client that I wanted to set up as a DMZ host for internet connection #1. The problem, of course, was that I did not have an access point to use with network 1. So, on a whim, I decided to get creative and uplink the switches, thus creating one big broadcast domain with multiple subnet. Yes, I know this is never a good idea, but I wanted to see if I could make it work. Anyway, as long as all the hosts are assigned static IP's, everything works fine!! The problem is that we have two DHCP servers handing out IP addresses in two different subnets, and the clients don't know which one to listen to.
So that is how this post got started--I just wanted to know what a host would do in such a situation, and whether you could configure a host to listen preferentially to one DHCP server.
Again, yes this is a horrible mess, but I wanted to get to the nitty gritty here and figure out the technical details.