You are correct in your guess.
ATAPI and IDE are he same.
Do make sure that you set the jumpers on the drives for master - slave correctly.
If your DVD writer is dual purpose and writes CDR as well, you will be able to dispense with your CDRW.
If you go ahead post back reference connecting to which cable.
Regards Brian j
PS I'm sure some more tech able people will give you more advice.