Mulitiple wifi connections on Macbook
If the external wifi device shows up in system preferences network pane, ensure that the internal adapter is above it in the "set service order" dialog (get to this by clicking the gear icon near the bottom left corner and selecting "set service order")

Do note that some external wifi devices do not show up in system preferences or don't obey this setting, so YMMV. If it doesn't show up or doesn't obey the service order, your only option would probably be to change it manually in Terminal.

Note that if you don't have a valid IP address on one of them it will automatically be lower than one that does.

Also, if the two networks also share the same IP scheme (ex 192.168.1.xxx), the computer might be getting confused by this. The way you describe this makes me think this is the problem, but service order is also a distinct possibility.