Having two SSIDs means your clients will not automatically roam between the APs, they will stay locked to whichever one you join them to. They will still be part of the same network once connected of course, if the APs are connected together.
If they have the same SSID then the client should connect to whatever AP has the strongest signal. For this to work both APs need to have the same security settings.
In both cases the router and AP should be using channels at least six apart from each other to reduce interference.
If your laptop struggles to connect to the router but works fine off the Airport AP and you can confirm all the encryption settings are indeed correct then I'd suggest something as simple as a firmware upgrade for the router, and possibly a driver update on the laptop. It is quite possible it will fix the issue of WPA dropping off radomly as well.