There is a difference between the encryption used for WPA (TKIP) and WPA2 (AES).
Kindly check whether the Data Encryption type is AES on your daughter's laptop (I assume the machine with WPA2-PSK is able to connect wirelessly to the Internet)
You can do this as follows: (I am again assuming that you are using Windows Wireless Client)
Right Click on the My Network Places Icon on the Windows Desktop and select Properties.
In the window that opens, right click the wireless network connection and again select properties.
Select the Wireless Networks Tab. Select Network Authentication as WPA2-PSK and Data Encryption as AES.
Re-enter the network key (twice)
Click ok and ok, once more.
You should be ready to go now, just disable and re-enable the wireless connection.
In case you are not using the Windows wireless Client, you'll have to tell us which client you are using (it will most likely be something that came with your wireless adapter).
Hope this helps.
Warm regards,
Sarang