getting iPad to recognize phone number

Here's my issue:

Sending iMessages from my phone or laptop to my wife's phone, laptop, and iPad work fine, but when she messages me back it gets split into two different conversations (one for the iPad, one for the phone). Interestingly, when I use the Messages app on my laptop, the two conversations are merged beautifully. Both my wife's details (cell number and email address) are in the same contact card on my phone.

My wife's iPad is not set up to send from her phone number. I cannot figure out how to do this. I've tried all the things suggested online (toggling iMessage on/off, signing out and back in again etc) but nothing has worked. All my messages (whether from phone or laptop) originate from my phone number. Are there any fixes to this, i.e., how can I get my wife's iPad, or more specifically her Apple ID, to sync with her phone number? No matter what we try we just don't get a prompt for this. The only options she can see in settings-messages-send/receive are email addresses.

Thanks.