iMessage is not operating uniformly.

bjohnston wrote:

No. We don’t share the same Apple ID account.

In that case both of you should do this...

do all 8 steps here, don't miss any out

1.    Settings, Apps, Messages,

2.    turn off iMessage   

3.    Settings, Apps, Facetime,

4.    Turn off Facetime,   

5.    Power down the phone

6.    Turn on the phone again 

7.    Settings, Apps, Messages, turn on iMessage,   (allow a moment to activate).

8.    Settings, Apps, Facetime, turn on Facetime

At the end ensure that only your number appears in your send/receive addresses in those settings

To activate iMessage and FaceTime using your Phone number

1. First, check to know whether you have an SMS plan enabled for at least one SMS*** with your carrier. Contact your Carrier (Cellular Service Provider), the agency that issued the SIM to you
2. If your iPhone is used with a carrier not found in the wireless carrier articles, make sure you can send and receive international SMS. (One international SMS*** Only)
3. If you can't turn on or sign in to iMessage or FaceTime - Apple ...

*** You may not have an SMS plan (Domestic & International) enabled by your carrier for the SIM/eSIM that you use on your device. Apple Inc. does not provide SMS services.

Check on her phone:

Settings → Apple ID (top) → Name, Phone Numbers, Email

• Make sure the “Reachable At” section shows her numbers/emails only.
• Make sure her phone number is checked under iMessage:
• 
  
  • Settings → Messages → Send & Receive → “You can receive iMessages to and reply from”

bjohnston wrote:

No. We don’t share the same Apple ID account.

OK. That's good. If messages aren't coming in to your wife's phone, it would be a carrier issue, whether AT&T wants to admit that or not. Is your son also on iPhone? When you check Settings > Apps > Messages > You can be reached at, is her cell number checked?

By chance do you and your wife share the same Apple Account?