|DSi's support WPA not lites!|
Well, that's pretty important information then. I looked over your initial post and it said. "I’d like to keep it that way but it will not work with my Nintendo DS. which as you can see for yourself, didn't include that important little tidbit of info.
Regardless, I know nothing about nintendo DS's to begin with.
As to your initial question about setting up two routers, here's how to do it.
First, Check on your main router and ascertain what IP subnet you're using. It's most likely a Class C private (something like 192.168.0.0) and then check the DHCP settings for your router and check what the scope is. By default, most SOHO router's use 100 to 199 (192.168.0.100 to 192.168.0.199).
Once you know that, you can choose an IP that's outside the DHCP scope. Using the same IP's as I did above, you would choose something like: 192.168.0.25. This is going to be the IP you'll be using on the second router.
Now, get a crossover cable and connect the two devices from LAN port on the first router to a LAN port on the second router.
Someone's likely to point out you don't have to use a crossover cable. That's correct, you may not have to. So, if you don't have one, and can't afford one, try a regular network cable. If it works, fine. If not, then you will have to get a crossover. I always use crossovers when connecting like devices because it's better that way.
Having said that, I reiterate, you're going to go from LAN port to LAN port
On the second router, connect to it's management interface and give it that IP you picked out (192.168.0.25) and also the same subnet mask as the other router. Your "Default Gateway" IP will be the IP of your first router.
You can also define a DHCP scope on the second router. Make sure that scope is outside the scope of the DHCP on your first router. Say, something like 50 to 60 (192.168.0.50 to 192.168.0.60)
Now, configure your WEP and test.
Keep in mind, WEP is easily cracked so I recommend when you're not actively gaming with your DS lite, power that second router off so you don't get hacked.