It should also come back to your phone whether it is connected to Cellular data or Wi-Fi. Make sure in your Messages settings, you have set it up to receive messages from both your number and your iTunes account. Same on your iPad. Once both are set up the same, both should receive replies, and either should be able to send a response.
If you do not have a data plan on your phone, then Messages will send to the device currently connected (your iPad at home on Wi-Fi) and not your disconnected iPhone.