Hello Kilmarlake,
We understand that your wife's Photo Stream is not updating. To ensure that we're on the correct path, go to Settings > [your name] > iCloud > Photos and verify if she has the option to Upload to My Photo Stream or turn on iCloud Photos. If she has the option to Upload to My Photo Stream, be sure that it is enabled and complete the following steps:
1. Tap Settings > Wi-Fi on all of your devices. Check that Wi-Fi is on and you have an internet connection.
2. On the device that captured the photo that you're looking for, close the Camera app. (Nothing uploads to My Photo Stream until you do.)
3. See if your iOS device is below 20% battery power. If it is, My Photo Stream disables itself temporarily to save battery life.
Click here for more details: If My Photo Stream isn't updating
If she has iCloud Photos enabled, she can check the status of her uploads by completing the following steps:
1. Open the Photos app.
2. Select the Library tab, then tap All Photos.
3. Scroll to the bottom to see the status bar.
Check out this resource for further assistance: Get help with iCloud Photos
Let us know if this helps.
Cheers!