Good morning Chatool,
Welcome to the Apple Support Communities!
I understand you would like to know if you can access Apple Music on more than one device using your Apple ID. Based on the devices you suggested above, you would not be able to stream Apple Music on your wife's iPad if her Apple ID is different than yours. Unlike the computer, you cannot have multiple accounts on an iPad.
However, if you have an Apple Music Family subscription, your wife can listen to the Apple Music catalog using her unique Apple ID on her iPad at the same time you are listening to the music that you like using your Apple ID on your iPhone or Mac.
Add and download music, shows, and movies from the Apple Music catalog
If you subscribe to Apple Music, you can add songs, albums, playlists, shows, and movies to your Library from anywhere in Apple Music. You can also download your content so that you can listen to or watch it when you're not connected to the Internet.
Before you add or download content, make sure to turn on iCloud Music Library on all of your devices.
When you add content to your Library, you can access it across all of your other devices, as long as you're signed in to all of your devices with the same Apple ID.
Get an Apple Music Family subscription
Each member of an Apple Music Family subscription gets unlimited access to the entire Apple Music catalog, music recommendations tailored to their personal music tastes, and access to their own iCloud Music Library, which makes it possible for them to listen to their music on all of their favorite devices.
Use Apple Music on your iPhone, iPad, iPod touch, or Android phone
Take care.