Hello tbreilly,
Welcome to Apple Support Communities.
We understand that your wife is part of your Family Sharing group but unable to access Apple Music. We are happy to help.
These steps may help. Please try the steps here: If you can't find your family's shared content - Apple Support
"Check your Family Sharing settings
Make sure that you're using the same Apple ID for Family Sharing and Media & Purchases. And make sure that purchase sharing is turned on. Then ask your family members to check their settings too.
On your iPhone or iPad with iOS 16 or later
- Go to Settings > Family.
- Tap your name.
- Make a note of which Apple ID is listed.
- Tap Purchases.
- Tap Apple ID for Purchases and make sure that you're signed in with with the same Apple ID that you use for Family Sharing. If not, tap Share using secondary Apple ID and enter the Apple ID and password for that Apple ID. "
Let us know if you have further questions.
Take care.