...
Is this because of the way I have the network setup? Would I be better off having the internet come into a wireless router, turning off the dhcp, and hooking up the server and two clients to the lan ports? If it would work that way, it would be nice, as doing so would probably solve the problem with the PDA.
...
From what I can tell your current network setup is perfect the way it is.
I'm not sure what problem you're exactly having with the PDA. Maybe you just need to connect the switch to the LAN port of the wireless router and leave it's WAN port unused as that is likely to "firewall" your PDA from the Core.