So in the watch wallet I would create an offline transaction and then sign this on the Offline computer and the broadcast it to the recipient is that correct?
Exactly. Keep in mind that you can't broadcast signed transaction on the offline computer so you have to move it to the other computer.
Do you know why the balance in the watch only wallet does not appear in the BitCoin Core wallet ?
Are you sure that your Bitcoin Core synchronizes correctly with the network? I am quite sure that there was a command which allowed you to check if your private key is related to a certain Bitcoin address. I can't recall it right now. Did you use your public key to create the watch only wallet?