Tracking wife's iPhone on separate Apple ID

If you are both in the same “Family Sharing” group, look in …

… Settings -> Family -> Location Sharing

Family Sharing gives you extra features over-and-above “regular contact” sharing.

e.g. The ability to more easily “Find” each other’s devices; including “Play a Sound” and to “Mark as Lost”

Set up Family Sharing - Apple Support

Have her read:

Share your location in Find My on iPhone - Apple Support

If she shares her location, you can view location using the findmy app or iCloud.com/find.

Ask her to share her location with you.